{"id":43,"date":"2020-01-29T15:04:04","date_gmt":"2020-01-29T20:04:04","guid":{"rendered":"http:\/\/pages.charlotte.edu\/borisvainberg\/?page_id=43"},"modified":"2024-12-10T17:07:53","modified_gmt":"2024-12-10T22:07:53","slug":"publications","status":"publish","type":"page","link":"https:\/\/pages.charlotte.edu\/borisvainberg\/publications\/","title":{"rendered":"Publications"},"content":{"rendered":"\n
Books:<\/h5>\n\n\n\n
    \n
  1. Asymptotic Methods in Equations of Mathematical Physics, 1982 (in Russian).<\/li>\n\n\n\n
  2. Asymptotic Methods in Equations if Mathematical Physics (revised and expanded English version), Gordon and Breach Science Publishers, New York–London, 1989<\/li>\n\n\n\n
  3. Large Time Asymptotic Expansion of the Solutions of Exterior Boundary Value Problems for Hyperbolic Equations and Quasiclassical Approximations, Chapter in “Partial Differential Equations, V”, 1999, Speinger-Verlag, Berlin-Heidelberg-New York, Series: Encyclopeadia of Math. Sciences.<\/li>\n\n\n\n
  4. Linear Water Waves: A Mathematical Approach, Cambridge University Press, 2002 (with N. Kuznetsov and V. Mazya)<\/li>\n<\/ol>\n\n\n\n

    <\/p>\n\n\n\n

    Articles:<\/h5>\n\n\n\n

    <\/p>\n\n\n\n

    186. Propagation of acoustic waves in 3D periodic media: Dispersion, clusters, and local gaps, (2024), submitted (with Y. Godin), http:\/\/dx.doi.org\/10.2139\/ssrn.4865864<\/a>
    185. Spectral Analysis of Lattice Schrodinger-Type Operators Associated with the Nonstationary Anderson Model and Intermittency, (2024), submitted, (with D. Han and S. Molchanov)     arxiv.org\/abs\/2403.13977<\/a>
    184. Local gaps in three-dimensional periodic media. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, accepted (2024), (with Yu. Godin)     arXiv:2403.01689<\/a>
    183. Propagation of acoustic waves in 3D periodic media containing small inclusions: I. Dispersion analysis and formation of clusters, II. Determination of gaps.p.474-477. Proc. of the 16th Intern. Conf. on Math. and Numerical Aspects of Wave Propagation. Berlin, Germany (2024)    , (with Yu. Godin)<\/a>
    182. Propagation and dispersion of Bloch waves in periodic media with soft inclusions. J. Math. Phys., 65 (5), 051505 (2024), (with Yu. Godin)     arxiv.org\/abs\/2304.03453<\/a>
    181. Negative eigenvalues of non-local Schrodinger operators with sign-changing potentials, Proceedings of AMS, 151, No 11, 4757-4770 (2023) (with S. Molchanov)     arXiv:2209.12124<\/a>
    180. Absolutely continuous and pure point spectra of discrete operators with sparse potentials, Math. Methods in Applied Sciences, 2022; 1-12. doi:10.1002\/mma.8435 (with S. Molchanov, O. Safronov),     arXiv:2110.08684<\/a>
    179. The slowdown of group velocity in periodic waveguides. Mechanics and Physics of Structured Media, pp.191 – 200 (2022)     (with Yu. Godin), <\/a>arXiv:1912.06964<\/a>
    178. Clusters of Bloch waves in three-dimensional periodic media, Proceedings A., Proceedings R. Soc., A., 478, issue 2267 (2022), 20220519     (with Yu. Godin) <\/a>arXiv:2207.08296<\/a>
    177. Global limit theorem for parabolic equations with a potential, SIAM Journal on Mathematical Analysis 54 (2022), no 2, 2097-2113 (with L. Koralov),     arXiv:2106.13307<\/a>.
    176. On the Near-Critical Behavior of Continuous Polymers, Pure and Applied Functional Analysis,     7 (2022), no 2, 691-702<\/a> (with L. Koralov, S. Molchanov) arXiv:2012.01607<\/a>.
    175.     The Radius of a Polymer at a Near-Critical Temperature, <\/a>Applicable Analysis, 101 (2022) no 8, 2797-2804, (with L. Koralov, S. Molchanov) <\/a>arXiv:2008.04493v1<\/a>.
    174. Dispersion of waves in two and three-dimensional periodic media, Waves in Random and Complex Media, 32, No. 3, pp. 1150-1173 (2022) (with Yu. Godin),     arXiv:1905.12529<\/a>
    173. Stanislav Alekseevich Molchanov (on his 80th birthday), Russ Math Surv, 76 (5), (2021), 943-949 (with M. Aizenman et al.).
    172.     Global solution of the initial value problem for the focusing Davey-Stewartson II system, Pure and Applied Functional Analysis, 2 (5), (2020), 369-389 <\/a>(with E. Lakshtanov), arXiv:1803.00955<\/a>.<\/strong>
    171.     On critical value of the coupling constant in exterior elliptic problems, Applicable Analysis, 101, No. 1, 108-117 (2020), (with R. Puri), <\/a>arXiv:1812.10132<\/a>.
    170. Obituary of Alexander Gordon, J. of Spectral Theory, 9, no 4 (2019), 1157-1164, (with S. Jitomirskaya, S. Molchanov, B. Simon)     arXiv:1910.08374<\/a>
    169. Designing lasing and perfectly absorbing potentials, Physical Review A, Vol. 99, No. 4, (2019),     043838, <\/a>(with V. Konotop, E. Lakshtanov) arXiv:1812.05499<\/a>.
    168. Dispersive and effective properties of two-dimensional periodic media, Proceedings of the Royal Society A, Vol. 475,     issue 2227, 20180298, 17 pp. <\/a>(2019) (with Yu. Godin) arXiv:1805.02636<\/a>.167. Population dynamics with moderate tails of the underlying random walk, SIAM Journal on Math. Analysis, 51(3), (2019), 1824-1835 <\/a>(with S. Molchanov) arXiv:1805.03133<\/a>.
    166. Solution of the initial value problem for the focusing Davey-Stewartson II system, Contemporary Math, American Math. Society, Providence, RI 2019, accepted, (with E. Lakshtanov),     arXiv:1604.01182<\/a>.
    165. Uniqueness in the inverse conductivity problem for complex-value Lipschitz conductivities in the plane, SIAM Journal on Mathematical Analysis, 49(5), (2017), 3766-3775 (with J. Tejero, E. Lakshtanov), arXiv:1703.04905
    164. Recovery of $L_p$ potential in the plane, Journal of Inverse and Ill-Posed Problems, 25, No 5 (2017), 633-651, (with E. Lakshtanov), \u00a0arXiv:1608.05807.
    163. Spectral analysis of non-local Schrodinger operators, Journal of\u00a0Funct. Analysis, 273, No\u00a03 (2017), 1020-1048 (with Yu. Kondratiev and S. Molchanov),     arXiv:1603.01626<\/a>.
    162. Intermittency for branching walks with heavy tails, Stochastics and Dynamics, 17, No. 6 (2017) 1750044 (with A. Getan, S. Molchanov),     arXiv:1509.02214<\/a>
    161. Uniqueness in potential scattering with reduced near field data, Communications in PDE, 42:6, (2017), 943-949, (with E. Lakshtanov),     arXiv:1503.07106<\/a>
    160. Recovery of interior eigenvalues from reduced near field data, (with E. Lakshtanov), Applicable Analysis, 96, (2017), No 15, 2425-2552,     arXiv:1501.03748<\/a>
    159. A test for the existence of exceptional points in the Faddeev scattering problem, Theoretical and Mathematical Physics, 190, No 2, (2017), p 77-90, (with E. Lakshtanov),     arXiv:1407.1548<\/a>.
    158. Long-wave approximation for the effective dielectric tensor of periodic materials, Proceedings of 2016 URSI International Symposium of Electromagnetic Theory (EMTS), Espoo, Finland, 553-556. (with Yu Godin)
    157. On reconstruction of complex-valued once differentiable conductivities, J. Spectral Theory, 6, No 4 (2016), 881-902 (with E. Lakshtanov),     arXiv:1511.0878<\/a>0<\/a>
    156. A global Riemann-Hilbert problem for two-dimensional inverse scattering at fixed energy, Rend. Inst. Mat. Univ. Trieste, 48, (2016), 1-26, Special issue in honor of G. Alessandrini’s 60th birthday, (with E. Lakshtanov, R. Novikov),     https:\/\/arxiv.org\/abs\/1509.06495<\/a>
    155. Sharp Weyl Law for Signed Counting Function of Positive Interior Transmission Eigenvalues,\u00a0SIAM Journal on Math. Analysis,\u00a047(4), (2015) 3212-3234\u00a0(with E. Lakshtanov)\u00a0    arXiv:1401.6213<\/a>.
    154. Global limit theorems on the convergence of multidimensional random walks to stable processes, Stochastics and Dynamics,\u00a015, (2015), 1550024 (with A. Agbor, S. Molchanov)\u00a0    arXiv:1405.2487<\/a>
    153. On\u00a0mathematical foundation of the Brownian motor theory, J.\u00a0Funct. Analysis 267, N 6 (2014), 1725-1750, \u00a0    arXiv:1304.6790<\/a>, (with L. Koralov and S. Molchanov)
    152. Weyl type bound on positive Interior Transmission Eigenvalues, Communications in PDE, 39, N 9, (2014), 1729-1740, (with E. Lakshtanov),\u00a0    arXiv:1307.4503<\/a>
    151. Lyapunov exponent of the random Schrodinger operator with white or short-range correlated noise potential, Russian Journal of Mathematical Physics, Vol. 20, No. 4, (2013), 438-452. (with Yu. Godin and S. Molchanov)
    150. Applications of elliptic operator theory to the isotropic interior transmission eigenvalue problem, Inverse\u00a0Prroblems, 29, No 10 (2013) 104003 (with E. Lakshtanov)     arXiv:1212.6785<\/a>
    149. Non-random perturbations of the Anderson Hamiltonian in the 1-D case, Applicable Analysis, 92, No. 8, 1755-1765 (2013) (with J. Holt and S. Molchanov)     arXiv:1205.1038<\/a>
    148. On\u00a0the negative spectrum of the hierarchical Schrodinger operator, J.\u00a0Funct. Analysis, 263 No 9 (2012), 2676-2688,\u00a0(with S. Molchanov)\u00a0    arXiv:1206.4019<\/a>
    147. Bounds on positive interior transmission eigenvalues, Inverse Problems, 28 (2012) 105005 (with E. Lakshtanov)\u00a0    arXiv:1206.3782<\/a>
    146. A priori estimates for high frequency scattering by obstacles of arbitrary shape, Comm. Partial Differential Equations, 37, No 10 (2012), 1789-1804\u00a0(with E. Lakshtanov)\u00a0    arXiv:1011.5261<\/a>
    145.\u00a0Remarks on interior transmission eigenvalues, Weyl formula and branching billiards, Journal of Physics A: Mathematical and Theoretical, 45, No 12 (2012), 125202 (with E. Lakshtanov)     arXiv:1112.0891<\/a>
    144. Ellipticity in the interior transmission problem in anisotropic media, SIAM Journal on Mathematical Analysis, 44, No 2, (2012), \u00a01165 -1174 (with E. Lakshtanov)\u00a0    arXiv:1108.5987<\/a>
    143. Bargmann type estimates of the counting function for general Schrodinger operators, (2012), Journal of Mathematical Sciences, 184, No 4 (2012),\u00a0457-508 (with S. Molchanov)\u00a0    arXiv:1201.3135<\/a>
    142. High frequency scattering by a classically invisible body, SIAM Journal of Applied Mathematics, 72, No 2 (2012) 646-669 (with E. Lakshtanov and B.D.Sleeman)\u00a0    arXiv:1008.3469<\/a>
    141. Scattering of solitons for coupled wave-particle equations, Journal of Math. Analysis and Application, 389 (2012) No 2, 713-740 (with V. Imaikin, A. Komech)\u00a0    arXiv:1006.2618<\/a>
    140. The effect of disorder on the wave propagation in one-dimensional periodic optical systems, Waves in Random and Complex Media, 21 (2011) No 1, 135-150 (with Yu. Godin and S. Molchanov)\u00a0    arXiv:1110.4132<\/a>
    139. Non-random perturbations of the Anderson Hamiltonian, Journal of Spectral Theory, 1, No 1, (2011), 179-196 (with S. Molchanov)\u00a0    arXiv:1002.4220<\/a>
    138.\u00a0Resonance regimes of scattering by small bodies with impedance boundary conditions, Journal of Physics A: Mathematical and Theoretical, 43 (2010), No 41, 415205 (with E. Lakshtanov).\u00a0    arXiv:1001.4754<\/a>
    137. On general Cwikel-Lieb-Rozenblum and Lieb-Thirring inequalities, in Around the research of Vladimir Maz’ya III, Editor A. Laptev, Int. Math. Ser. (N.Y.) 13, Springer, 2010, \u00a0201-246 (with S. Molchanov) (see\u00a0    arXiv:0812.2968<\/a>).
    136. On the determination of the boundary impedance from the far field pattern, SIAM Journal on Appl. Math., 70, (2010),\u00a02273-2280\u00a0(with Yu. Godin).\u00a0    arXiv:0908.0359<\/a>
    135. A solvable model for homopolymers and self-similarity near the critical point, Random Operators and Stochastic Equations, 18, No 1, (2010), 73-95 (with M. Cranston, et al). (see\u00a0    arXiv:0906.2816<\/a>)
    134. Wave propagation in periodic networks of thin fibers, Waves in Random and Complex Media, 20, No 2, (2010), 260-275 (with S. Molchanov). (    arXiv:0908.0156<\/a>)
    133. Propagation of Waves in Networks of Thin Fibers, in Integral Methods in Science and Engineering, Vol. I, Birkhauser Verlag, (2010),\u00a0255-278. (with S. Molchanov). (see\u00a0    arXiv:0902.1567<\/a>)
    132. On negative spectrum of Schrodinger type operators, in Operator Theory: Advances and Applications, Birkhauser Verlag, Vol. 193, (2009), 197-214 (with S. Molchanov).
    131. Continuous Model for\u00a0Homopolymers, J. Functional Analysis, 256 (2009) no. 8, 2656-2696 (with M. Cranston et al) (see\u00a0    arXiv:0902.2830<\/a>)
    130. On Dispersive Properties of Discrete 2D Schrodinger and Klein-Gordon Equations, J. Functional Analysis, 254, no. 8 (2008),\u00a02227–2254.\u00a0(with\u00a0A.\u00a0Komech\u00a0and\u00a0E.\u00a0Kopylova).
    129. A simple method for solving the inverse scattering problem for the difference Helmholtz equation, Inverse problems, 24 no. 2 (2008)\u00a0025007\u00a0(with Yu. Godin).
    128. The inverse scattering problem for the difference operators: the decomposition method, Journal of Physics: Conference Series, 135, (2008), 012044\u00a0(with Yu. Godin).
    127. Eigenvalues estimates for random Schrodinger operators, Proceedings of AMS, 136, no. 11 (2008),\u00a03921–3929.\u00a0(with\u00a0O.\u00a0Safronov) (see\u00a0    mp_arc\u00a007 116<\/a>).
    126. Vladimir\u00a0Gilelevich\u00a0Mazya\u00a0(on his 70th<\/sup>\u00a0birthday), Russian Math. Surveys, 63, no. 1, (2008), 189-196. (with\u00a0M.\u00a0Agranovich\u00a0et al.)
    125. Laplace operator in networks of thin fibers: spectrum near the threshold, in Stochastic analysis in mathematical physics, 69-93, World Sci. Publ., Hackensack, NJ, 2008. (with S. Molchanov), (see arXiv:0704.2795).
    124. Stanislav\u00a0Molchanov,\u00a0CRM Proceedings and Lecture Notes, V.42 (2007),\u00a0ix-x (with V.\u00a0Jakshic).
    123. Transmission through a randomly perturbed periodic medium, Proceedings of the conference WAVES 2007,\u00a0Reading,\u00a0UK.\u00a0pp.53-56.
    122. Wave propagation in 1D randomly perturbed periodic medium, Waves in Random and Complex Media, 17 (3), pp 381-395 (2007), (with Y. Godin and\u00a0S. Molchanov).
    121. Scattering solutions in networks of thin fibers: small diameter\u00a0asymptotics, Comm. in Math. Physics, V 273 (2007), pp 533-559 (with\u00a0S. Molchanov), (see\u00a0    arXiv:math-ph\/0609021<\/a>).
    120. On scattering of solitons for wave equation coupled to a particle, CRM Proceedings and Lecture Notes, V.42 (2007), pp249-271 (with V.\u00a0Imaikin\u00a0and A.\u00a0Komech\u00a0).
    119. On the influence of random perturbations on the propagation of waves described by a Schrodinger operator, CRM Proceedings and Lecture Notes, V. 42 (2007), pp 167-179. (with\u00a0Y. Godin and\u00a0S. Molchanov).
    118. On the structure of\u00a0eigenfunctions\u00a0corresponding to embedded eigenvalues of locally perturbed periodic graph operators, Comm. in Math. Physics, 268 (2006), pp 673-686, (with P.\u00a0Kuchment) (see\u00a0    arXiv: math-ph\/0511084<\/a>).
    117. On soliton\u00a0asymptotics\u00a0and scattering for a nonlinear wave-particle system, Comm. in Math. Physics, V. 268, No 2, (2006), pp 321-367 (with V.\u00a0Imaikin\u00a0and A.\u00a0Komech) (see\u00a0    arXiv: math-ph\/0609205<\/a>).
    116.\u00a0Transition from a network of thin fibers to the quantum graph: an explicitly solvable model, Contemporary Mathematics, v. 415, AMS (2006), pp 227-240 (with\u00a0S.\u00a0Molchanov) (see\u00a0    arXiv: math-ph\/0605037<\/a>).
    115. Localization on\u00a0Avron-Exner-Last Graphs: I. Local Perturbations, Contemporary Mathematics, v. 415, AMS (2006), pp 81-92 (with K. Chen and\u00a0S. Molchanov).
    114. Slowing down and reflection of waves in truncated periodic media, Journal of Functional Analysis, 231 No 2 (2006), pp 287-311 (with\u00a0S. Molchanov). (see\u00a0    arXiv:math\/0503075<\/a>)
    113. Large time behavior of the solutions to the difference wave operators, Comm. PDE, 31 No 3, (2006), pp 397-416 (with H.\u00a0Islami\u00a0). (see\u00a0    arXiv:math\/0503128<\/a>)
    112. Slowing down of the wave packets in quantum graphs. Waves in Complex and Random Media, 15, No 1 (2005), pp. 101-112 (with\u00a0S. Molchanov)
    111. Slowdown of the wave packages in finite slabs of periodic media, Waves in Random Media, 14, No 3 (2004), pp. 411-423 (with\u00a0S. Molchanov)
    110. Schrodinger operators with matrix potentials. Transition from the absolutely continuous to the singular spectrum, Journal of Functional Analysis, 215 (2004), 111-129 (with\u00a0S. Molchanov) (see\u00a0    arXiv:math-ph\/0308012<\/a>)
    109. The spectrum of water waves produced by moving point sources, and a related inverse problem, Wave Motion, 38, (2003), 345-354 (with H.\u00a0Hellsten, and V.\u00a0Maz’ya)
    108. Quasi 1D localization: deterministic and random potentials, Markov Processes and Related Fields, 9, No 4, (2003), 687-708 (with W.\u00a0Kirsh\u00a0et al)
    107. Radiation conditions for the difference Schrodinger operators, Applicable Analysis, 80, 525-556 (2001) (with W.\u00a0Shaban).
    106. First\u00a0KdV\u00a0integrals and absolutely continuous spectrum for 1-D Schrodinger operator, Comm. of Math. Phys., 216, 195-213 (2001) (with S. Molchanov and M.\u00a0Novitskii).
    105. On\u00a0absence of embedded eigenvalues for Schrodinger operators with perturbed periodic potentials, Comm. PDE, 25, 1809-1826, (2000) (with P.\u00a0Kuchment). (see\u00a0    arXiv:math-ph\/9904016<\/a>)
    104. Spectrum of multidimensional Schrodinger operators with sparse potentials, Analytical and Computational Methods in Scattering and Applied Mathematics, Editors F.\u00a0Santosa, I.\u00a0Stakgold, Chapman and Hall\/CRC, 2000, pp 231-253 (with S. Molchanov).
    103. Scattering on the system of the sparse bumps: multidimensional case, Applicable Analysis, Vol. 71, (1999), pp167-185 (with\u00a0S. Molchanov).
    102. Resonances for\u00a0multistratified\u00a0acoustic waveguides, Applicable Analysis, Vol. 71, (1999), pp 413-440 (with Y.\u00a0Dermenjian\u00a0and O. Poisson).
    101. On\u00a0Maz’ya’s\u00a0works in the linear theory of water waves, Operator Theory, Advances and Applications, Vol 109,\u00a0Birkhauser\u00a0Verlag, 1999, pp 17-34 (with N.\u00a0Kuznetsov).
    100. Asymptotic methods for an optimal antenna problem, SIAM Journal of Applied Math., Vol. 59, No 1, pp 242-260, (1998) (with T. Angell and R.\u00a0Kleinman)
    99. On spectral\u00a0asymptotics\u00a0for domains with fractal boundaries of cabbage type, Mathematical physics, Analysis and Geometry, Vol 1, pp 145-170 (1998) (with\u00a0S. Molchanov).
    98. On embedded eigenvalues of perturbed periodic Schrodinger operators, Spectral and Scattering Theory (Newark, DE, 1997) pp67-75, Plenum, N.-Y., 1998 (with P.\u00a0Kuchment)
    97. Long time behavior of solutions to linear and nonlinear hyperbolic problems, Modern Mathematical Methods in Diffraction Theory and its Appl. in Engineering (Proceedings of the\u00a0Sommerfeld\u00a096 Workshop,\u00a0Germany), pp 234-250, Lang, Frankfurt am Main, 1997.
    96. On\u00a0spectral\u00a0asymptotics\u00a0for domains with fractal boundaries, Comm. Math. Physics, Vol 183, pp 85-117 (1997) (with S. Molchanov).
    95. Asymptotic approximations for optimal conformal antennas, in “Ultra-Wideband, Short-Pulse Electromagnetics 3”, Edited by\u00a0C.Baum, L. Carin, A. Stone, Plenum Press, pp 177-183, 1997.(with T. Angell and R.\u00a0Kleinman).
    94. On\u00a0asymptotic stability of stationary solutions to nonlinear wave and Klein-Gordon equations, Arch. Rat. Mech. and Anal., Vol 134, pp 227-248 (1996) (with A.\u00a0Komech).
    93. Full low-frequency asymptotic expansion for second order elliptic equations in two dimensions, Math. Methods in the Appl. Sciences, Vol. 17, pp 989-1004 (1994), (with R.\u00a0Kleinman).
    92. Asymptotic approximation of optimal solutions of an acoustic radiation problem, Inverse Scattering and Potential Problems in Mathematical Physics (Oberwolfach, 1993), pp 5-16 ,\u00a0Lang, Frankfurt am Main (1993) (with T. Angell and R.\u00a0Kleinman).
    91. On ship waves, Wave motion, Vol. 18, pp 31-50 (1993) (with\u00a0V.Maz’ya).
    90. On the local energy of solutions of exterior mixed problems that are periodic with respect to $t$, Trans. Moscow Math. Soc., pp 191-216, (1993).
    89. Full low-frequency asymptotic expansion for elliptic equations of second order, Second Int. Conference on Math.\u00a0and\u00a0Numerical Aspects of Wave Propagation, Edited by R.\u00a0Kleinman..[at\u00a0al.],\u00a0SIAM, pp 296-301, 1993 (with R.\u00a0Kleinman).
    88. Scattering of waves in a medium depending periodically on time,\u00a0Asterisque, Vol 210, pp 327-340, (1992).
    87. On\u00a0uniqueness and asymptotic behavior of solutions of the Neumann-Kelvin problem, Abstracts of Seventh International Workshop on Water Waves and Floating Bodies, Val de\u00a0Reuil, France, pp 125-128, (1992), (with V.\u00a0Maz’ja).
    86. Direct method of research of the scattering problem in a medium depending periodically on time, Abstract of International Conference on Differential Equations and Mathematical Physics,\u00a0Georgia, TECH-UAB, pp 68-69, (1992).
    85. Scattering by periodically moving obstacles, Math.\u00a0USSR\u00a0Sbornik, Vol 73, No 1, pp 289-304, (1992).
    84. On\u00a0ship waves, Preprint of\u00a0Linchoping\u00a0University, Sweden, (1991), pp 1-48 (with V.\u00a0Maz’ja).
    83. Scattering of waves by periodically moving bodies, Proceedings of Symposium Dedicated to the Century of Academician N.\u00a0Muskhelishvili, Continuum Mechanics and Related Problems of Analysis, pp 121, 1991.
    82. On local energy of solutions of exterior mixed periodic in time problems, Trans. Moscow Math. Soc., Vol 54, (1991) (in Russian).
    81. Mikhail\u00a0Vasilevich\u00a0Fedoryuk, Russian Math.\u00a0Serveys, Vol 46, pp237-240 (1991) (with V. Arnold and others).
    80. On the asymptotic\u00a0behaviour\u00a0as $ t \\to\\\u00a0infty\u00a0$ of solutions of the exterior mixed problem depending periodically on time, Conference on Differential Equations and Their\u00a0 Applications, (Ruse, Bulgaria, 1989), pp 311-320, Tech. Univ. Ruse, 1991.
    79. Scattering on periodically moving obstacles,\u00a0Uspehi\u00a0Mat.\u00a0Nauk, Vol 45, No 4, pp 131-132, (1990), (in Russian).
    78. Asymptotic behavior as $ t \\to\\\u00a0infty\u00a0$ of solutions of exterior mixed problems periodic with respect to time, Mathematical Notes, Vol 47, No 4, pp 315-322, (1990).
    77. Asymptotic expansion of the spectral function of elliptic operators in\u00a0R^n, Journal of Soviet Mathematics, Vol 47, No 3, pp 2537-2546, (1989).
    76. Asymptotic Methods in Equations of Mathematical Physics, Monograph, Gordon and Breach Science Publishers,\u00a0New York–London, 1989.
    75. On the decay of local energy for exterior mixed periodic in time problems,\u00a0Uspehi\u00a0Mat.\u00a0Nauk, Vol 43, No 4, pp 177, (1988), (in Russian).
    74. Exterior boundary problems and scattering theory,\u00a0Encyclopaedia\u00a0of Mathematical Sciences,\u00a0Viniti-Springer Publishers, Vol 30, pp 190-206, 1987.
    73. Asymptotic\u00a0behaviour\u00a0as $ t \\to\\\u00a0infty\u00a0$ of solutions of exterior mixed problems for hyperbolic equations, and\u00a0quasiclassics,\u00a0Encyclopaedia\u00a0of Mathematical Sciences,\u00a0Viniti-Springer Publishers, Vol 34, pp 57–92, 1987.
    72. Long-wave approximation in a problem of the interaction of an electromagnetic field with a conducting\u00a0body ,\u00a0Uspehi\u00a0Mat.\u00a0Nauk, Vol 42, No 4, pp 141-142, (1987), (in Russian).
    71. Long-wave approximation in a problem of interaction of electromagnetic field with a conducting body, Modern Problems of Mathematical Physics, 151-158, Tbilisi, April, 1987, (in Russian).
    70. Limit-absorption principle,\u00a0Encyclopaedia\u00a0of Mathematics, Kluwer Academic Publishers, Vol 5, pp 451-452, 1987.
    69. Fourier integral operator,\u00a0Encyclopaedia\u00a0of Mathematics, Kluwer Academic Publishers, Vol 4, pp 70-73, 1987.
    68. Parametrix\u00a0and\u00a0asymptotics\u00a0of the spectral function of differential operators in\u00a0R^n, Math.\u00a0USSR\u00a0Sbornik, Vol 58, No 1, pp 245-265, (1987).
    67. Local decrease of energy of solutions of hyperbolic systems, Journal of Soviet Mathematics, Vol 32, No 3, pp 272-280, (1986).
    66. Parametrix\u00a0and “almost spectral” expansion for differential operators in\u00a0R^n,\u00a0Uspehi\u00a0Mat.\u00a0Nauk, Vol 40, No 5, pp 303-304, (1985), (in Russian).
    65. On the\u00a0parametrix\u00a0and\u00a0asymptotics\u00a0of the spectral function of differential operators in\u00a0R^n, Soviet Math.\u00a0Dokl.,\u00a0Vol 31, No 3, pp 456-460, (1985).
    64. Characteristic Cauchy problem for a hyperbolic equation, Journal of Soviet Mathematics, Vol 31, No 4, pp 3135-3147, (1985), (with V.\u00a0Maz’ja).
    63. A complete asymptotic expansion of the spectral function of second order elliptic operators in\u00a0R^n, Math.\u00a0USSR\u00a0Sbornik, Vol 51, No 1, pp 191-206, (1985).
    62. Global\u00a0parametrix\u00a0of the Cauchy problem for hyperbolic equations,\u00a0Uspehi\u00a0Mat.\u00a0Nauk, Vol 39, No 4, pp 101, (1984), (in Russian).
    61. On a method of impedance measuring by oscillating plates and casings, Soviet Applied. Mechanics, Vol 48, No 1, pp 92-97, (1984), (with V.\u00a0Krutin).
    60. Limit-amplitude principle, Mathematical\u00a0Encyclopaedia, Vol 4, Soviet\u00a0Encyclopaedia\u00a0Publishers, 1984, p 572, (in Russian).
    59. Complete asymptotic expansion of a spectral function of elliptic operators in\u00a0R^n, Moscow Univ. Math. Bull., Vol 38, (1983).
    58. Solution of transport equations for charged particles in electric field, Protection from Ionizing Radiation of Nuclear Machinery, Vol 3,\u00a0Tbilisi, TGU, 1983, pp 59-65, (with Yu.\u00a0Egorov, K.\u00a0Truchanov), (in Russian).
    57. Scattering of charged particles in a thin layer of matter with electric field, Protection from Ionizing radiation of Nuclear Machinery, Vol 3, Tbilisi, TGU, 1983, pp 52-58, (with V.\u00a0Grebenev, K.\u00a0Truchanov), (in Russian).
    56. Asymptotic Methods in Equations of Mathematical Physics, Monograph,\u00a0Moscow\u00a0State\u00a0University\u00a0Publishers, 1982, (in Russian).
    55. Quasiclassical\u00a0asymptotic\u00a0behaviour\u00a0of scattering amplitude, Application of methods of theory of functions and functional analysis to the problems of mathematical physics, Yerevan Univ. Publishers, 1982, pp 68-70, (in Russian).
    54. Diagnostics of physical and mechanical properties of medium by oscillations of bordering casings, Waves and Diffraction, Proceedings of the 8th All-Union symposium on Diffraction and Propagation of Waves, Vol 1, 1981, (with V.\u00a0Krutin), (in Russian).
    53. Solution of transport equations for charged particles in electric field, Third All-Union Conference on Protection from Ionizing Radiation of Nuclear Machinery, 1981, p 10, (with Yu.\u00a0Egorov, K.\u00a0Truchanov), (in Russian).
    52. Scattering of charged particles in a thin layer of matter with electric field, Third All-Union conference on Protection from Ionizing Radiation of Nuclear Machinery, 1981, p 9, (with\u00a0K.Truchanov, V.\u00a0Grebenev), (in Russian).
    51. Short-wave asymptotic\u00a0behaviour\u00a0of scattering amplitude of waves in inhomogeneous medium,\u00a0Chechoslovak\u00a0Conference on Differential Equations and their Applications, Abstracts,\u00a0Bratislava,\u00a0Equadiff\u00a05, 1981, pp 234-236.
    50. Measuring of elastic characteristics of medium with arbitrarily oscillating casings,\u00a0Uspehi\u00a0Mat.\u00a0Nauk, Vol 36, No\u00a04.,\u00a0p 209, (1981), (with V.\u00a0Krutin), (in Russian).
    49.\u00a0Stabilization of the solutions of exterior problems for hyperbolic systems, Partial Differential Equations (Proc. Conf., Novosibirsk, 1978),\u00a0Nauka\u00a0Publishers, 1980, pp 109-110, (in Russian).
    48. Stabilization of the solutions of exterior problems for hyperbolic systems,\u00a0Uspehi\u00a0Mat.\u00a0Nauk, Vol 35, No 4, p 159, (1980), (in Russian).
    47. On\u00a0the characteristic Cauchy problem for a hyperbolic equation, Russian Math. Surveys, Vol 35, No 1, pp 237–238, (1980), (with V.\u00a0Maz’ja).
    46. Large time asymptotic\u00a0behaviour\u00a0of solutions of exterior problems for hyperbolic systems, All Union Conference on Asymptotic Methods in the Theory of Singularly\u00a0Perturbated\u00a0Equations, Proceedings, Alma-Ata, 1979, pp 98-100, (in Russian).
    45. Method of canonical operator, Theory of Propagation of Waves in Inhomogeneous and Nonlinear Mediums, Radio-Electronics Publishers, 1979, pp 144-187, (in Russian).
    44. On a method of computation of flows of particles in systems of magnetic protection, Problems of Dosimetry and Protection from Radiation, Vol 17,\u00a0Automizdat\u00a0Publishers, 1978, pp 149-154, (with Yu.\u00a0Egorov\u00a0and others), (in Russian).
    43. On differential equations describing the motion of a car on a curve, Proceedings of Scientific and Technical Conference of Moscow State University and\u00a0Lihachev\u00a0Automobile plant, 1978, (with Yu.\u00a0Egorov), (in Russian).
    42. Stationary problems of scattering theory and large time\u00a0behaviour\u00a0of solutions of nonstationary problems, Proceedings of All-Union Conference on Partial Differential Equations, (Moscow State University, Moscow, 1976). Moscow State Univ. Publishers,\u00a0Moscow, 1978, pp 58-62, (in Russian).
    41. Short-wave approximations in the problem of scattering of plane waves in inhomogeneous medium, Theory of Diffraction and Propagation of Waves, Vol 2 (Proceedings of 7th All-Union Symposium on Diffraction and Propagation of Waves), pp 22-25, 1977, (in Russian).
    40. Quasiclassical\u00a0approximation in stationary scattering problems, Functional Analysis and it’s Applications, Vol 11, No 4, pp 247-257, (1977).
    39. Quasiclassical\u00a0approximations in scattering problems,\u00a0Uspehi\u00a0Mat.\u00a0Nauk, Vol 32, No 1, pp 236-237, (1977), (in Russian).
    38. The All-Union Conference-Seminar of heads of university mathematics departments,\u00a0Uspehi\u00a0Mat.\u00a0Nauk, Vol 31, No 2, pp 247-253, (1976), (with B. V.\u00a0Gnedenko\u00a0and others), (in Russian).
    37. On\u00a0the method of stationary phase, Moscow Univ. Math. Bull., Vol 31, No 1, pp 50-58, (1976).
    36. Short-wave asymptotic\u00a0behaviour\u00a0of solutions of steady-state problems, Proceedings of Conference on Differential Equations and their Applications,\u00a0Rusa\u00a0(Bulgaria), 1975.
    35. On short-wave asymptotic\u00a0behaviour\u00a0of solutions of steady-state problems and the asymptotic\u00a0behaviour\u00a0as $ t \\to\\\u00a0infty\u00a0$ of solutions of time-dependent problems, Russian Math. Surveys, Vol 30, No 2, pp 1-58, (1975).
    34. The principle of limiting amplitude,\u00a0Izv.\u00a0Vysov,\u00a0Matematika, No 2, pp 12-23, (1974), (in Russian).
    33. Behaviour\u00a0for large time of solutions of the Klein–Gordon equation, Trans. Moscow Math. Soc., Vol 30, pp 139–159, (1974).
    32. On short-wave asymptotic\u00a0behaviour\u00a0of solutions of steady-state problems and the asymptotic\u00a0behaviour\u00a0as $ t \\to\\\u00a0infty\u00a0$ of solutions of time-dependent problems, Colloquium on Differential Equations,\u00a0Kestely\u00a0(Hungary), Summaries, 1974.
    31. On\u00a0a point source in an inhomogeneous medium, Math.\u00a0USSR\u00a0Sbornik, Vol 23, No 1, pp 123-148, (1974).
    30. On\u00a0the problem of a point source in an inhomogeneous medium, Moscow Univ. Math. Bull., Vol 29, No 1\/2, pp 21-27, (1974).
    29. On\u00a0exterior elliptic problems\u00a0polynomially\u00a0depending on a spectral parameter, and the asymptotic\u00a0behaviour\u00a0for large time of solutions of nonstationary problems, Math.\u00a0USSR\u00a0Sbornik, Vol 21, No 2, pp 221-239, (1973).
    28. Large time\u00a0behaviour\u00a0of solutions of the Klein-Gordon equation,\u00a0Uspehi\u00a0Mat.\u00a0Nauk, Vol 28, No 4, pp 213-214, (1973), (in Russian).
    27. On the problem of the steady–state oscillations of a fluid layer of variable depth, Trans. Moscow Math. Soc., Vol 28, pp 56–73, (1973), (with V. G.\u00a0Maz’ja).
    26. On\u00a0the plane problem of the motion of a body immersed in a fluid, Trans. Moscow Math. Soc., Vol 28, pp 33-55, (1973), (with V. G.\u00a0Maz’ja).
    25. On\u00a0some stationary problems in the linear theory of surface waves, Soviet Physics\u00a0Dokl., 17, pp 640–643, (1972\/73), (with V. G.\u00a0Maz’ja).
    24. On\u00a0eigenfunctions\u00a0of an operator corresponding to the poles of the analytic continuation of the\u00a0resolvent\u00a0through the continuous spectrum, Math.\u00a0USSR\u00a0Sbornik, Vol 16, No 2, pp 307–322, (1972).
    23. On\u00a0the principle of limiting amplitude, Math.\u00a0USSR\u00a0Sbornik, Vol 15, No 1, pp 89–108, (1971).
    22. Behaviour\u00a0of the solution of the Cauchy problem for a hyperbolic equation as $ t \\to\\\u00a0infty\u00a0$ ,\u00a0Math.\u00a0USSR\u00a0Sbornik, Vol 7, No 4, pp 533–567, (1969).
    21. On\u00a0the analytical properties of the\u00a0resolvent\u00a0for a certain class of operator-pencils, Math.\u00a0USSR\u00a0Sbornik, Vol 6, No 2, pp 241-273, (1968).
    20.\u00a0On\u00a0elliptic problems in unbounded domains, Math.\u00a0USSR\u00a0Sbornik, Vol 4, No 3, pp 419-444, (1968).
    19. The solutions of elliptic equation with constant coefficients and right-hand side increasing at infinity, Moscow Univ. Math. Bull., No 1, pp 41–48, (1968).
    18. Uniformly\u00a0nonelliptic\u00a0problems II, Math.\u00a0USSR\u00a0Sbornik, Vol 2, No 1, pp 111-133, (1967), (with V.\u00a0Grushin).
    17. Uniformly\u00a0nonelliptic\u00a0problems I, Math.\u00a0USSR\u00a0Sbornik, Vol 1, No 4, pp 543-568, (1967), (with V.\u00a0Grushin).
    16. Uniformly\u00a0noncoercive\u00a0problems for elliptic equations, Soviet Math.\u00a0Dokl.,\u00a0Vol 8, No 1, pp 154-158, (1967), (with V.\u00a0Grushin).
    15. Uniformly\u00a0nonelliptic\u00a0systems of singular\u00a0integro–differential equations on compact manifolds, Soviet Math.\u00a0Dokl.,\u00a0Vol 7, No 1, pp 118-120, (1967), (with V.\u00a0Grushin).
    14. On\u00a0exterior elliptic problems, Second Bulgarian Math. Congress, 1967, pp 22-26 (in Russian).
    13. The strong form of\u00a0Huyghens’ principle for a class of differential operators with constant coefficients, Trans. Moscow Math. Soc., Vol 16, pp 163-196, (1967), (with S. G.\u00a0Gindikin).
    12. Principles of radiation, limiting absorption and limiting amplitude in the general theory of partial differential equations, Russian Math. Surveys, Vol 21, No 3, pp 115-193, (1966).
    11. Uniformly\u00a0noncoercive\u00a0problems for elliptic equations, Theses of short scientific reports at International Mathematical Congress, Section 7, Moscow 1966, pp 22, (with V.\u00a0Grushin).
    10. Radiation conditions for equations of high order and the generalized principle of limiting absorption, Proceedings of Third All-Union Symposium on Diffraction of Waves, 1964, pp 31-33, (in Russian).
    9. \u00a0Hypoelliptic\u00a0equations in the whole space and the principle of limiting absorption, Soviet Math.\u00a0Dokl.,\u00a0Vol 5, No 2, pp 317–320, (1964).
    8. \u00a0Correctly stated problems with the conditions in the infinity for the\u00a0hypoelliptic\u00a0operators defined in the whole space, Outlines of Joint Soviet-American Symposium on Partial Differential Equations, Novosibirsk (1963), Acad. Sci. USSR,\u00a0SibireanBranch, Publishers, Moscow, 1963, pp 361-368, (with V.\u00a0Grushin).
    7. Some problems for hypo-elliptic equations which are well-posed in the entire plane, Mat.\u00a0Sbornik, Vol 62, No 2, pp 186–248, (1963), (in Russian).
    6. On\u00a0conditions of\u00a0Sommerfeld\u00a0type,\u00a0Uspehi\u00a0Mat.\u00a0Nauk.,\u00a0Vol 18, No 2, pp 169-171, (1963), (in Russian).
    5. On\u00a0conditions of\u00a0Sommerfeld\u00a0type for elliptic operators of any order, Proceedings of Second All-Union Symposium on Diffraction of Waves, 1962, pp 39-41, (in Russian).
    4. Asymptotic representation of fundamental solutions of hyperbolic equations, the problem extending throughout the whole space with conditions at infinity, Soviet Math.\u00a0Dokl.,\u00a0Vol 3, No 4, pp 914-916, (1962).
    3. Asymptotic\u00a0behaviour\u00a0of fundamental solutions of hyperbolic equations involving two variables and a problem with conditions imposed at infinity, Soviet Math.\u00a0Dokl.,\u00a0Vol 3, No 3, pp 828-832, (1962).
    2. The existence and uniqueness of a solution of certain elliptic equations over the whole plane, Soviet Math.\u00a0Dokl.,\u00a0Vol 3, No 1, pp 5-7, (1962).
    1. The asymptotic\u00a0behaviour\u00a0of Green’s function for the\u00a0Sobolev-Gal’pern\u00a0equation, Soviet Math.\u00a0Dokl.,\u00a0Vol 2, No 1, pp 147–150, (1961).<\/p>\n\n\n\n

    <\/p>\n\n\n\n

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    Books: Articles: 186. Propagation of acoustic waves in 3D periodic media: Dispersion, clusters, and local gaps, (2024), submitted (with Y. Godin), http:\/\/dx.doi.org\/10.2139\/ssrn.4865864185. Spectral Analysis of Lattice Schrodinger-Type Operators Associated with the Nonstationary Anderson Model and Intermittency, (2024), submitted, (with D. Han and S. Molchanov) arxiv.org\/abs\/2403.13977184. Local gaps in three-dimensional periodic media. Proceedings of the Royal […]<\/p>\n","protected":false},"author":2990,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-43","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/pages.charlotte.edu\/borisvainberg\/wp-json\/wp\/v2\/pages\/43","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pages.charlotte.edu\/borisvainberg\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/pages.charlotte.edu\/borisvainberg\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/pages.charlotte.edu\/borisvainberg\/wp-json\/wp\/v2\/users\/2990"}],"replies":[{"embeddable":true,"href":"https:\/\/pages.charlotte.edu\/borisvainberg\/wp-json\/wp\/v2\/comments?post=43"}],"version-history":[{"count":18,"href":"https:\/\/pages.charlotte.edu\/borisvainberg\/wp-json\/wp\/v2\/pages\/43\/revisions"}],"predecessor-version":[{"id":117,"href":"https:\/\/pages.charlotte.edu\/borisvainberg\/wp-json\/wp\/v2\/pages\/43\/revisions\/117"}],"wp:attachment":[{"href":"https:\/\/pages.charlotte.edu\/borisvainberg\/wp-json\/wp\/v2\/media?parent=43"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}