## Babich, Vasiliĭ Mikhaĭlovich

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 Author ID: babich.vasilii-mikhailovich Published as: Babich, V. M.; Babich, Vasilii M.; Babich, Vassily M.; Babich, Vasily M.; Babich, Vasilii; Babich, Vassilii M.; Babitsch, W. M.; Babbich, V. M.; Babič, V. M.; Babih, V. M. more...less Homepage: http://www.pdmi.ras.ru/eng/perso/vbabich.php External Links: MGP · Wikidata · Math-Net.Ru · GND
 Documents Indexed: 200 Publications since 1953, including 9 Books 46 Contributions as Editor · 3 Further Contributions Biographic References: 4 Publications Co-Authors: 109 Co-Authors with 104 Joint Publications 2,653 Co-Co-Authors
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### Serials

 53 Journal of Mathematical Sciences (New York) 23 Journal of Soviet Mathematics 23 Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta Imeni V. A. Steklova 11 Vestnik Leningradskogo Universiteta. Matematika, Mekhanika, Astronomiya 11 Zapiski Nauchnykh Seminarov POMI 6 St. Petersburg Mathematical Journal 5 Wave Motion 4 Russian Mathematical Surveys 4 Russian Journal of Mathematical Physics 3 Uspekhi Matematicheskikh Nauk [N. S.] 3 Matematicheskiĭ Sbornik. Novaya Seriya 3 Algebra i Analiz 3 SIAM Journal on Applied Mathematics 3 Vestnik Leningrad University. Mathematics 3 Doklady Akademii Nauk SSSR. Novaya Seriya 2 Doklady Akademii Nauk SSSR 2 Journal of Applied Mathematics and Mechanics 2 Soviet Mathematics. Doklady 2 Vestnik Leningradskogo Universiteta. Seriya 1. Matematika, Mekhanika, Astronomiya 2 Mathematics of the USSR, Sbornik 2 Soviet Physics. Doklady 2 U.S.S.R. Computational Mathematics and Mathematical Physics 2 Integral Transforms and Special Functions 2 PMM, Journal of Applied Mathematics and Mechanics 2 Problemy Matematicheskoĭ Fiziki 2 Proceedings of the Steklov Institute of Mathematics 1 Fluid Dynamics 1 Mathematical Notes 1 Revue Roumaine de Mathématiques Pures et Appliquées 1 Geophysical Journal International 1 Soviet Applied Mechanics 1 Functional Analysis and its Applications 1 Siberian Mathematical Journal 1 Teoriya Funktsiĭ, Funktsional’nyĭ Analiz i ikh Prilozheniya 1 Itogi Nauki i Tekhniki. Seriya Sovremennye Problemy Matematiki. Fundamental’nye Napravleniya 1 Mathematische Lehrbücher und Monographien. I. Abteilung: Mathematische Lehrbücher 1 Trudy Matematicheskogo Instituta Imeni V. A. Steklova 1 Translations. Series 2. American Mathematical Society 1 Monographs and Research Notes in Mathematics
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### Fields

 113 Partial differential equations (35-XX) 77 Mechanics of deformable solids (74-XX) 46 General and overarching topics; collections (00-XX) 39 Fluid mechanics (76-XX) 34 Optics, electromagnetic theory (78-XX) 23 History and biography (01-XX) 21 Geophysics (86-XX) 19 Ordinary differential equations (34-XX) 6 Operator theory (47-XX) 6 Differential geometry (53-XX) 5 Special functions (33-XX) 5 Approximations and expansions (41-XX) 5 Mechanics of particles and systems (70-XX) 3 Global analysis, analysis on manifolds (58-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 1 Functions of a complex variable (30-XX) 1 Integral transforms, operational calculus (44-XX) 1 Integral equations (45-XX) 1 Numerical analysis (65-XX) 1 Quantum theory (81-XX)

### Citations contained in zbMATH Open

90 Publications have been cited 540 times in 430 Documents Cited by Year
Asymptotische Methoden in Problemen der Diffraktion von Kurzwellen. Methode der Etalon-Probleme. (Asimptoticeskie metody v zadacah difrakcii korotkih voln. Metod etalonnyh zadac.). Zbl 0255.35002
Babich, V. M.; Buldyrev, V. S.
1972
The boundary-layer method in diffraction problems. Transl. by E. F. Kuester. Zbl 0411.35001
Babich, V. M.; Kirpichnikova, N. Ya.
1979
The space-time ray method. Linear and nonlinear waves. (Prostranstvenno-vremennoj luchevoj metod. Linejnye i nelinejnye volny.) Zbl 0678.35002
Babbich, V. M.; Buldyrev, V. S.; Molotkov, I. A.
1985
Short-wavelength diffraction theory. Asymptotic methods. Transl. from the Russian by E. F. Kuester. Zbl 0742.35002
Babič, V. M.; Buldyrev, V. S.
1991
On evaluation of the diffraction coefficients for arbitrary ”nonsingular” directions of a smooth convex cone. Zbl 0992.78016
Babich, Vassilii M.; Dement’ev, Daniel B.; Samokish, Boris A.; Smyshlyaev, Valery P.
2000
The complex space-time ray method and ”quasi-photons”. Zbl 0477.35025
Babich, V. M.; Ulin, V. V.
1981
The linear equations of mathematical physics. Edited by S. G. Mikhlin. (Линеиные уравнения математическои физики.) Zbl 0122.33001
Babich, V. M.; Kapilevich, M. B.; Mikhlin, S. G.; Natanson, G. I.; Riz, P. M.; Slobodetskii, L. N.; Smirnov, M. M.
1964
Elastic waves: high frequency theory. Zbl 1402.74003
Babich, Vassily M.; Kiselev, Aleksei P.
2018
The short wave asymptotic form of the solution for the problem of a point source in an inhomogeneous medium. Zbl 0167.24301
Babich, V. M.
1968
Methode der Grenzschicht in Beugungsproblemen. (Metod pogranicnogo sloya v zadachahk difrakoij.). Zbl 0317.35001
Babich, V. M.; Kirpichnikova, N. Ya.
1974
On the diffraction of high-frequency waves by a cone of arbitrary shape. Zbl 0968.74551
Babich, Vasilii; Dement’ev, Daniel; Samokish, Boris
1995
On Budaev and Bogy’s approach to diffraction by the 2D traction-free elastic wedge. Zbl 1223.74022
Kamotskii, V. V.; Fradkin, L. Ju.; Samokish, B. A.; Borovikov, V. A.; Babich, V. M.
2006
Scattering problem for the Schrödinger equation in the case of a potential linear in time and coordinate. I: Asymptotics in the shadow zone. Zbl 0584.35019
Babich, V. M.; Smyshlyaev, V. P.
1986
Eigenfunctions concentrated in a neighborhood of a closed geodesic. Zbl 0207.11001
Babich, V. M.
1968
Complex space-time ray method and ”quasiphotons”. Zbl 0532.35007
Babich, V. M.; Ulin, V. V.
1984
Propagation of Love waves along the surface of an anisotropic body of an arbitrary shape. Zbl 0662.73020
Azhotkin, V. D.; Babich, V. M.
1987
Non-geometrical waves - are there any? An asymptotic description of some ’non-geometrical’ phenomena in seismic wave propagation. Zbl 0704.73023
Babich, Vasily M.; Kiselev, Aleksey P.
1989
Zur Frage der Fortsetzung von Funktionen. Zbl 0050.06201
Babich, V. M.
1953
Über die Beschränktheit des Dirichletschen Integrals. Zbl 0072.05002
Slobodetskij, L. N.; Babich, V. M.
1956
The focussing problem and the asymptotic behavior of the spectral function of the Laplace-Beltrami operator. Zbl 0357.35020
Babich, V. M.; Levitan, B. M.
1976
The art of asymptotics. Zbl 0374.41013
Babich, V. M.; Buldyrev, V. S.
1977
The scattering problem for the Schrödinger equation with a potential linear in time and in space. II: Correctness, smoothness, behavior of the solution at infinity. Zbl 0621.35076
Babich, V. M.; Smyshlyaev, V. P.
1987
The multidimensional WKB method or ray method. Its analogs and generalizations. Zbl 0657.35119
Babich, V. M.
1988
Ausbreitung von Love- und Rayleigh-Wellen in einem schwach inhomogenen, geschichteten Medium. Zbl 0325.73032
Babich, V. M.; Chikhachev, B. A.
1975
Application of the method of two-scale expansions to the single-frequency problem of the theory of nonlinear oscillations. Zbl 0596.70027
Azhotkin, V. D.; Babich, V. M.
1985
The mathematical theory of diffraction ( a survey of some investigations carried out in the laboratory of mathematical problems of geophysics, Leningrad branch of the Mathematical Institute). Zbl 0850.01021
Babich, V. M.
1986
The focussing problem and asymptotic behavior of the spectral function of the Laplace-Beltrami operator. Zbl 0427.35051
Babich, V. M.; Levitan, B. M.
1978
The propagation of Rayleigh waves over the surface of a non-homogeneous elastic body with an arbitrary form. Zbl 0117.41707
Babich, V. M.; Rusakova, N. J.
1962
Problem of focusing and the asymptotics of the spectral function of the Laplace-Beltrami operator. I. Zbl 0514.35064
Babich, V. M.; Levitan, B. M.
1983
Hadamard’s ansatz, its analogs, generalizations, applications. Zbl 0779.35002
Babich, V. M.
1991
On the PC-ansatz. Zbl 1082.35048
Babich, V. M.
2004
The analytic extension of the resolvent of outer three-dimensional problems for Laplace operators in the second sheet. Zbl 0292.35064
Babich, V. M.; Grigor’eva, N. S.
1974
The Hadamard ansatz, its analogues, generalizations, and applications. Zbl 0791.35002
Babich, V. M.
1991
Complex ray solutions and eigenfunctions concentrated in a neighborhood of a closed geodesic. Zbl 0488.58025
Babich, V. M.; Ulin, V. V.
1982
Mathematical methods in the theory of elastic waves. Zbl 0496.73018
Babich, V. M.; Molotkov, I. A.
1977
The diffraction of a high-frequency acoustic wave by a narrow-angle absolutely rigid cone of arbitrary shape. Zbl 0885.76089
Babich, V. M.
1996
On Fock’s type asymptotics of Legendre functions. Zbl 0874.33010
Babich, V. M.; Cherednichenko, K. D.
1997
Boundary layer approach to describe an interference head wave. Zbl 1231.74219
Babich, Vasily M.
2009
A new approach to the problem of the Rayleigh wave propagation along the boundary of a non-homogeneous elastic body. Zbl 1163.74312
Babich, V. M.; Kirpichnikova, N. Ya.
2004
On the propagation of surface electromagnetic waves analogous to Rayleigh waves in the case of Leontovich boundary conditions. Zbl 1092.35108
Babich, V. M.; Kuznetsov, A. V.
2005
The space-time ray method and quasiphotons. Zbl 1176.81170
Babich, V. M.
2008
Mathematical problems in the theory of wave propagation. Part 24. Zbl 0924.00023
1997
On the scattering problem for the Schrödinger equation in case of a potential which is linear with respect to time and to the coordinate. II Correctness, smoothness, behaviour of the solution at infinity. Zbl 0606.35063
Babich, V. M.; Smyshlyaev, V. P.
1985
Fundamental solutions of the dynamical equations of elasticity for nonhomogeneous media. Zbl 0102.17202
Babich, V. M.
1961
An interference head wave (Buldyrev wave) and the locality principle. Zbl 1404.35161
Babich, V. M.; Matskovskiy, A.
2017
Existence theorem for the solution of Dirichlet and Neumann problems for the Helmholtz equation in the quasiperiodic case. Zbl 0683.35020
Babich, V. M.
1988
A hyperbolic equation with the large parameter lower terms and hierarchy of waves. Zbl 0827.35071
Babich, V. M.; Klimova, A. A.
1994
A ray description of all wavefields generated by a high-frequency point source near an interface. Zbl 1097.35521
Babich, Vassily M.; Kiselev, Aleksei P.; Lawry, James M. H.; Starkov, Alexander S.
2001
“Nongeometrical phenomena” in propagation of elastic surface waves. Zbl 1100.74032
Babich, V. M.; Kiselev, A. P.
2004
Selected works. Complex analysis. Mathematical theory of diffraction. (Izbrannye trudy. Kompleksnyj analiz. Matematicheskaya teoriya difraktsii). Compiled and with commentaries by V. M. Babich, N. K. Nikol’skij and V. P. Khavin. (Izbrannye trudy. Kompleksnyj analiz. Matematicheskaya teoriya difraktsii.) Zbl 0699.01037
Smirnov, V. I.
1988
Disk-shaped normal-rupture crack near the surface of a semiinfinite body with initial stresses. Zbl 0770.73059
Babich, V. M.; Guz’, A. N.; Nazarenko, V. M.
1991
Eigenoscillations of mechanical systems and the spectral theory of self-adjoint operators. Zbl 0930.47043
Babich, V. M.
1994
The long wave asymptotics in problems of scattering the elastic waves. Zbl 0624.73027
Babich, V. M.; Ivanov, M. I.
1986
Asymptotic solution of the problem of a point source of diffusion in a moving medium with low diffusion coefficients. Zbl 0625.35037
Babich, V. M.
1986
Scattering of a high-frequency wave by the vertex of an arbitrary cone (singular directions). Zbl 1003.78006
Babich, V. M.; Dement’ev, D. B.; Samokish, B. A.; Smyshlyaev, V. P.
2000
Complex ray solutions and eigenfunctions concentrated in a neighbourhood of a closed geodesic. Zbl 0476.58030
Babich, V. M.; Ulin, V. V.
1981
Focusing problem and the asymptotics of the spectral function of the Laplace-Beltrami operator. II. Zbl 0495.35066
Babich, V. M.
1982
The strict justification of the short-wave approximation in the three- dimensional case. Zbl 0391.35025
Babich, V. M.
1973
A high-frequency point source of oscillations near a concave mirror. Zbl 0401.35022
Babich, V. M.
1979
Asymptotic properties of solutions to some three-dimensional wave problems. Zbl 0401.35023
Babich, V. M.; Grigor’eva, N. S.
1979
Nonspectral singularities of Green’s function for the Helmholtz equation in the exterior of an arbitrary convex polygon. Zbl 0401.35031
Babich, V. M.; Grigor’eva, N. S.
1979
A point source of oscillation in a neighbourhood of a concave mirror. II. Zbl 0427.35006
Babich, V. M.
1979
On eigen oscillations of the multilayered resonator. Zbl 0231.35043
Babich, V. M.
1969
Über Eigenfunktionen, die in der Nähe einer abgeschlossenen Geodätischen konzentriert sind. Zbl 0164.13601
Babich, V. M.; Lazutkin, V. F.
1967
On the propagation of Love waves along the surface of a non-homogeneous elastic body of an arbitrary form. (Über die Fortpflanzung Lovescher Wellen entlang der Oberfläche eines inhomogenen elastischen Körpers beliebiger Form.) Zbl 0213.27405
Babich, V. M.; Kirpichnikova, N. Ya.
1969
Hadamard’s method and the asymptotics of the spectral function of a second-order differential operator. Zbl 0463.35060
Babich, V. M.
1980
The boundary layer approach to the description of an interference head wave. Zbl 1344.35008
Babich, V. M.
2015
Propagation of waves in piezoelectric layer with a weak horizontal nonhomogeneity. Zbl 0953.74560
Babich, Vasilii M.; Lukyanov, Valery V.
1997
On a scattering problem for the Schrödinger equation with a potential linear in both time and coordinate. Zbl 0653.35071
Babich, V. M.; Smyshlyaev, V. P.
1985
Orthogonal expansions and Fourier method. Textbook. (Ortogonal’nye razlozheniya i metod Fur’e. Uchebnoe posobie). Zbl 0513.34001
Babich, V. M.; Grigor’eva, N. S.
1983
On the scattering problem for the Schrödinger equation in the case of the potential which is linear with respect to time and the coordinate. I: Asymptotics in the shadow zone. Zbl 0557.35024
Babich, V. M.; Smyshlyaev, V. P.
1984
Asymptotic behavior relative to a large parameter of the solution of the Fock-Klein-Gordon equation in the case of a discontinuous initial condition. Zbl 0562.35012
Babich, V. M.
1985
Skin-effect in the case of a conductor of an arbitrary cross section. Zbl 0566.35087
Babich, V. M.
1985
Application of complex rays to the calculation of scalar ”non-geometric” waves. Zbl 0741.73039
Babich, V. M.
1990
The case of exact integrability of the equation for SH-waves. Zbl 0810.35130
Babich, V. M.
1992
Mathematical problems in the theory of wave propagation. Part 27. Transl. from the Russian. Zbl 0967.00035
2000
Arlen Mikhailovich Il’in. Zbl 1104.01309
Babich, V. M.; Kalyakin, L. A.; Ramazanov, M. D.; Rozov, N. Kh.
2002
To the problem on the asymptotics with respect to the indices of the associated Legendre function. Zbl 1104.33300
Babich, V. M.
2002
On the development of methods for problems of propagation and diffraction of waves by S. L. Sobolev. Zbl 0638.35069
Alekseev, A. S.; Babich, V. M.
1986
A formal method of construction of a short-wave asymptotic expression for Green’s function. Zbl 0228.35026
Babich, V. M.
1971
On quasiphotons of Rayleigh waves (anisotropic elastic body case). Zbl 1189.74064
Babich, V. M.; Poskryakov, A. V.
2006
Mikhail Shlemovich Birman (obituary). Zbl 1219.01025
Babich, V. M.; Buslaev, V. S.; Vershik, A. M.; Gindikin, S. G.; Kislyakov, S. V.; Laptev, A.; Marchenko, V. A.; Nikol’skii, N. K.; Pastur, L. A.; Plamenevskii, B. A.; Solomyak, M. Z.; Suslina, T. A.; Ural’tseva, N. N.; Faddeev, L. D.; Khavin, V. P.; Yafaev, D. R.
2010
Factorizability of matrix functions: a direct proof. Zbl 1206.30052
Babich, V. M.
2009
A class of topographical waveguides. Zbl 1210.35261
Babich, V. M.
2011
Scattering of high-frequency electromagnetic waves by the vertex of a perfectly conducting cone (singular directions). Zbl 1108.78007
Babich, V. M.; Dement’ev, D. B.; Samokish, B. A.; Smyshlyaev, V. P.
2002
A point source of electromagnetic waves in an inhomogeneous medium: a high frequency ansatz and the dual nonstationary singular solution. Zbl 1435.35370
Babich, V. M.
2019
On the asymptotics of Green’s functions for certain wave problems. I: Stationary case. Zbl 0249.35016
Babich, V. M.
1972
D. Ludwig’s method and the boundary-layer method in the problem of diffraction by a smooth body. Zbl 0337.35021
Babich, V. M.
1975
Solution of the diffraction problem of a plane wave by an impedance wedge (non-stationary case. Smirnov-Sobolev method). Zbl 1321.35123
Babich, V. M.
2015
Locality principle and a high-frequency asymptotics of an interference head wave. Zbl 1422.35010
Babich, V. M.
2019
A point source of electromagnetic waves in an inhomogeneous medium: a high frequency ansatz and the dual nonstationary singular solution. Zbl 1435.35370
Babich, V. M.
2019
Locality principle and a high-frequency asymptotics of an interference head wave. Zbl 1422.35010
Babich, V. M.
2019
Elastic waves: high frequency theory. Zbl 1402.74003
Babich, Vassily M.; Kiselev, Aleksei P.
2018
An interference head wave (Buldyrev wave) and the locality principle. Zbl 1404.35161
Babich, V. M.; Matskovskiy, A.
2017
The boundary layer approach to the description of an interference head wave. Zbl 1344.35008
Babich, V. M.
2015
Solution of the diffraction problem of a plane wave by an impedance wedge (non-stationary case. Smirnov-Sobolev method). Zbl 1321.35123
Babich, V. M.
2015
A class of topographical waveguides. Zbl 1210.35261
Babich, V. M.
2011
Mikhail Shlemovich Birman (obituary). Zbl 1219.01025
Babich, V. M.; Buslaev, V. S.; Vershik, A. M.; Gindikin, S. G.; Kislyakov, S. V.; Laptev, A.; Marchenko, V. A.; Nikol&rsquo;skii, N. K.; Pastur, L. A.; Plamenevskii, B. A.; Solomyak, M. Z.; Suslina, T. A.; Ural&rsquo;tseva, N. N.; Faddeev, L. D.; Khavin, V. P.; Yafaev, D. R.
2010
Boundary layer approach to describe an interference head wave. Zbl 1231.74219
Babich, Vasily M.
2009
Factorizability of matrix functions: a direct proof. Zbl 1206.30052
Babich, V. M.
2009
The space-time ray method and quasiphotons. Zbl 1176.81170
Babich, V. M.
2008
On Budaev and Bogy’s approach to diffraction by the 2D traction-free elastic wedge. Zbl 1223.74022
Kamotskii, V. V.; Fradkin, L. Ju.; Samokish, B. A.; Borovikov, V. A.; Babich, V. M.
2006
On quasiphotons of Rayleigh waves (anisotropic elastic body case). Zbl 1189.74064
Babich, V. M.; Poskryakov, A. V.
2006
On the propagation of surface electromagnetic waves analogous to Rayleigh waves in the case of Leontovich boundary conditions. Zbl 1092.35108
Babich, V. M.; Kuznetsov, A. V.
2005
On the PC-ansatz. Zbl 1082.35048
Babich, V. M.
2004
A new approach to the problem of the Rayleigh wave propagation along the boundary of a non-homogeneous elastic body. Zbl 1163.74312
Babich, V. M.; Kirpichnikova, N. Ya.
2004
“Nongeometrical phenomena” in propagation of elastic surface waves. Zbl 1100.74032
Babich, V. M.; Kiselev, A. P.
2004
Arlen Mikhailovich Il’in. Zbl 1104.01309
Babich, V. M.; Kalyakin, L. A.; Ramazanov, M. D.; Rozov, N. Kh.
2002
To the problem on the asymptotics with respect to the indices of the associated Legendre function. Zbl 1104.33300
Babich, V. M.
2002
Scattering of high-frequency electromagnetic waves by the vertex of a perfectly conducting cone (singular directions). Zbl 1108.78007
Babich, V. M.; Dement&rsquo;ev, D. B.; Samokish, B. A.; Smyshlyaev, V. P.
2002
A ray description of all wavefields generated by a high-frequency point source near an interface. Zbl 1097.35521
Babich, Vassily M.; Kiselev, Aleksei P.; Lawry, James M. H.; Starkov, Alexander S.
2001
On evaluation of the diffraction coefficients for arbitrary ”nonsingular” directions of a smooth convex cone. Zbl 0992.78016
Babich, Vassilii M.; Dement&rsquo;ev, Daniel B.; Samokish, Boris A.; Smyshlyaev, Valery P.
2000
Scattering of a high-frequency wave by the vertex of an arbitrary cone (singular directions). Zbl 1003.78006
Babich, V. M.; Dement&rsquo;ev, D. B.; Samokish, B. A.; Smyshlyaev, V. P.
2000
Mathematical problems in the theory of wave propagation. Part 27. Transl. from the Russian. Zbl 0967.00035
2000
On Fock’s type asymptotics of Legendre functions. Zbl 0874.33010
Babich, V. M.; Cherednichenko, K. D.
1997
Mathematical problems in the theory of wave propagation. Part 24. Zbl 0924.00023
1997
Propagation of waves in piezoelectric layer with a weak horizontal nonhomogeneity. Zbl 0953.74560
Babich, Vasilii M.; Lukyanov, Valery V.
1997
The diffraction of a high-frequency acoustic wave by a narrow-angle absolutely rigid cone of arbitrary shape. Zbl 0885.76089
Babich, V. M.
1996
On the diffraction of high-frequency waves by a cone of arbitrary shape. Zbl 0968.74551
Babich, Vasilii; Dement&rsquo;ev, Daniel; Samokish, Boris
1995
A hyperbolic equation with the large parameter lower terms and hierarchy of waves. Zbl 0827.35071
Babich, V. M.; Klimova, A. A.
1994
Eigenoscillations of mechanical systems and the spectral theory of self-adjoint operators. Zbl 0930.47043
Babich, V. M.
1994
The case of exact integrability of the equation for SH-waves. Zbl 0810.35130
Babich, V. M.
1992
Short-wavelength diffraction theory. Asymptotic methods. Transl. from the Russian by E. F. Kuester. Zbl 0742.35002
Babič, V. M.; Buldyrev, V. S.
1991
Hadamard’s ansatz, its analogs, generalizations, applications. Zbl 0779.35002
Babich, V. M.
1991
The Hadamard ansatz, its analogues, generalizations, and applications. Zbl 0791.35002
Babich, V. M.
1991
Disk-shaped normal-rupture crack near the surface of a semiinfinite body with initial stresses. Zbl 0770.73059
Babich, V. M.; Guz&rsquo;, A. N.; Nazarenko, V. M.
1991
Application of complex rays to the calculation of scalar ”non-geometric” waves. Zbl 0741.73039
Babich, V. M.
1990
Non-geometrical waves - are there any? An asymptotic description of some ’non-geometrical’ phenomena in seismic wave propagation. Zbl 0704.73023
Babich, Vasily M.; Kiselev, Aleksey P.
1989
The multidimensional WKB method or ray method. Its analogs and generalizations. Zbl 0657.35119
Babich, V. M.
1988
Existence theorem for the solution of Dirichlet and Neumann problems for the Helmholtz equation in the quasiperiodic case. Zbl 0683.35020
Babich, V. M.
1988
Selected works. Complex analysis. Mathematical theory of diffraction. (Izbrannye trudy. Kompleksnyj analiz. Matematicheskaya teoriya difraktsii). Compiled and with commentaries by V. M. Babich, N. K. Nikol’skij and V. P. Khavin. (Izbrannye trudy. Kompleksnyj analiz. Matematicheskaya teoriya difraktsii.) Zbl 0699.01037
Smirnov, V. I.
1988
Propagation of Love waves along the surface of an anisotropic body of an arbitrary shape. Zbl 0662.73020
Azhotkin, V. D.; Babich, V. M.
1987
The scattering problem for the Schrödinger equation with a potential linear in time and in space. II: Correctness, smoothness, behavior of the solution at infinity. Zbl 0621.35076
Babich, V. M.; Smyshlyaev, V. P.
1987
Scattering problem for the Schrödinger equation in the case of a potential linear in time and coordinate. I: Asymptotics in the shadow zone. Zbl 0584.35019
Babich, V. M.; Smyshlyaev, V. P.
1986
The mathematical theory of diffraction ( a survey of some investigations carried out in the laboratory of mathematical problems of geophysics, Leningrad branch of the Mathematical Institute). Zbl 0850.01021
Babich, V. M.
1986
The long wave asymptotics in problems of scattering the elastic waves. Zbl 0624.73027
Babich, V. M.; Ivanov, M. I.
1986
Asymptotic solution of the problem of a point source of diffusion in a moving medium with low diffusion coefficients. Zbl 0625.35037
Babich, V. M.
1986
On the development of methods for problems of propagation and diffraction of waves by S. L. Sobolev. Zbl 0638.35069
Alekseev, A. S.; Babich, V. M.
1986
The space-time ray method. Linear and nonlinear waves. (Prostranstvenno-vremennoj luchevoj metod. Linejnye i nelinejnye volny.) Zbl 0678.35002
Babbich, V. M.; Buldyrev, V. S.; Molotkov, I. A.
1985
Application of the method of two-scale expansions to the single-frequency problem of the theory of nonlinear oscillations. Zbl 0596.70027
Azhotkin, V. D.; Babich, V. M.
1985
On the scattering problem for the Schrödinger equation in case of a potential which is linear with respect to time and to the coordinate. II Correctness, smoothness, behaviour of the solution at infinity. Zbl 0606.35063
Babich, V. M.; Smyshlyaev, V. P.
1985
On a scattering problem for the Schrödinger equation with a potential linear in both time and coordinate. Zbl 0653.35071
Babich, V. M.; Smyshlyaev, V. P.
1985
Asymptotic behavior relative to a large parameter of the solution of the Fock-Klein-Gordon equation in the case of a discontinuous initial condition. Zbl 0562.35012
Babich, V. M.
1985
Skin-effect in the case of a conductor of an arbitrary cross section. Zbl 0566.35087
Babich, V. M.
1985
Complex space-time ray method and ”quasiphotons”. Zbl 0532.35007
Babich, V. M.; Ulin, V. V.
1984
On the scattering problem for the Schrödinger equation in the case of the potential which is linear with respect to time and the coordinate. I: Asymptotics in the shadow zone. Zbl 0557.35024
Babich, V. M.; Smyshlyaev, V. P.
1984
Problem of focusing and the asymptotics of the spectral function of the Laplace-Beltrami operator. I. Zbl 0514.35064
Babich, V. M.; Levitan, B. M.
1983
Orthogonal expansions and Fourier method. Textbook. (Ortogonal’nye razlozheniya i metod Fur’e. Uchebnoe posobie). Zbl 0513.34001
Babich, V. M.; Grigor&rsquo;eva, N. S.
1983
Complex ray solutions and eigenfunctions concentrated in a neighborhood of a closed geodesic. Zbl 0488.58025
Babich, V. M.; Ulin, V. V.
1982
Focusing problem and the asymptotics of the spectral function of the Laplace-Beltrami operator. II. Zbl 0495.35066
Babich, V. M.
1982
The complex space-time ray method and ”quasi-photons”. Zbl 0477.35025
Babich, V. M.; Ulin, V. V.
1981
Complex ray solutions and eigenfunctions concentrated in a neighbourhood of a closed geodesic. Zbl 0476.58030
Babich, V. M.; Ulin, V. V.
1981
Hadamard’s method and the asymptotics of the spectral function of a second-order differential operator. Zbl 0463.35060
Babich, V. M.
1980
The boundary-layer method in diffraction problems. Transl. by E. F. Kuester. Zbl 0411.35001
Babich, V. M.; Kirpichnikova, N. Ya.
1979
A high-frequency point source of oscillations near a concave mirror. Zbl 0401.35022
Babich, V. M.
1979
Asymptotic properties of solutions to some three-dimensional wave problems. Zbl 0401.35023
Babich, V. M.; Grigor&rsquo;eva, N. S.
1979
Nonspectral singularities of Green’s function for the Helmholtz equation in the exterior of an arbitrary convex polygon. Zbl 0401.35031
Babich, V. M.; Grigor&rsquo;eva, N. S.
1979
A point source of oscillation in a neighbourhood of a concave mirror. II. Zbl 0427.35006
Babich, V. M.
1979
The focussing problem and asymptotic behavior of the spectral function of the Laplace-Beltrami operator. Zbl 0427.35051
Babich, V. M.; Levitan, B. M.
1978
The art of asymptotics. Zbl 0374.41013
Babich, V. M.; Buldyrev, V. S.
1977
Mathematical methods in the theory of elastic waves. Zbl 0496.73018
Babich, V. M.; Molotkov, I. A.
1977
The focussing problem and the asymptotic behavior of the spectral function of the Laplace-Beltrami operator. Zbl 0357.35020
Babich, V. M.; Levitan, B. M.
1976
Ausbreitung von Love- und Rayleigh-Wellen in einem schwach inhomogenen, geschichteten Medium. Zbl 0325.73032
Babich, V. M.; Chikhachev, B. A.
1975
D. Ludwig’s method and the boundary-layer method in the problem of diffraction by a smooth body. Zbl 0337.35021
Babich, V. M.
1975
Methode der Grenzschicht in Beugungsproblemen. (Metod pogranicnogo sloya v zadachahk difrakoij.). Zbl 0317.35001
Babich, V. M.; Kirpichnikova, N. Ya.
1974
The analytic extension of the resolvent of outer three-dimensional problems for Laplace operators in the second sheet. Zbl 0292.35064
Babich, V. M.; Grigor&rsquo;eva, N. S.
1974
The strict justification of the short-wave approximation in the three- dimensional case. Zbl 0391.35025
Babich, V. M.
1973
Asymptotische Methoden in Problemen der Diffraktion von Kurzwellen. Methode der Etalon-Probleme. (Asimptoticeskie metody v zadacah difrakcii korotkih voln. Metod etalonnyh zadac.). Zbl 0255.35002
Babich, V. M.; Buldyrev, V. S.
1972
On the asymptotics of Green’s functions for certain wave problems. I: Stationary case. Zbl 0249.35016
Babich, V. M.
1972
A formal method of construction of a short-wave asymptotic expression for Green’s function. Zbl 0228.35026
Babich, V. M.
1971
On eigen oscillations of the multilayered resonator. Zbl 0231.35043
Babich, V. M.
1969
On the propagation of Love waves along the surface of a non-homogeneous elastic body of an arbitrary form. (Über die Fortpflanzung Lovescher Wellen entlang der Oberfläche eines inhomogenen elastischen Körpers beliebiger Form.) Zbl 0213.27405
Babich, V. M.; Kirpichnikova, N. Ya.
1969
The short wave asymptotic form of the solution for the problem of a point source in an inhomogeneous medium. Zbl 0167.24301
Babich, V. M.
1968
Eigenfunctions concentrated in a neighborhood of a closed geodesic. Zbl 0207.11001
Babich, V. M.
1968
Über Eigenfunktionen, die in der Nähe einer abgeschlossenen Geodätischen konzentriert sind. Zbl 0164.13601
Babich, V. M.; Lazutkin, V. F.
1967
The linear equations of mathematical physics. Edited by S. G. Mikhlin. (Линеиные уравнения математическои физики.) Zbl 0122.33001
Babich, V. M.; Kapilevich, M. B.; Mikhlin, S. G.; Natanson, G. I.; Riz, P. M.; Slobodetskii, L. N.; Smirnov, M. M.
1964
The propagation of Rayleigh waves over the surface of a non-homogeneous elastic body with an arbitrary form. Zbl 0117.41707
Babich, V. M.; Rusakova, N. J.
1962
Fundamental solutions of the dynamical equations of elasticity for nonhomogeneous media. Zbl 0102.17202
Babich, V. M.
1961
Über die Beschränktheit des Dirichletschen Integrals. Zbl 0072.05002
Slobodetskij, L. N.; Babich, V. M.
1956
Zur Frage der Fortsetzung von Funktionen. Zbl 0050.06201
Babich, V. M.
1953
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### Cited in 94 Serials

 80 Journal of Soviet Mathematics 77 Journal of Mathematical Sciences (New York) 41 Wave Motion 24 Journal of Applied Mathematics and Mechanics 12 Russian Journal of Mathematical Physics 11 Journal of Computational Physics 11 Functional Analysis and its Applications 10 Mathematical Notes 9 Theoretical and Mathematical Physics 8 St. Petersburg Mathematical Journal 7 Prikladnaya Matematika i Mekhanika 7 Soviet Applied Mechanics 5 Fluid Dynamics 5 International Applied Mechanics 4 Journal of Mathematical Analysis and Applications 4 Journal of Mathematical Physics 4 Proceedings of the Steklov Institute of Mathematics 3 Communications in Mathematical Physics 3 Advances in Mathematics 3 Fuzzy Sets and Systems 3 Rendiconti del Seminario Matematico della Università di Padova 3 Siberian Mathematical Journal 3 Zeitschrift für Analysis und ihre Anwendungen 3 Sibirskiĭ Zhurnal Industrial’noĭ Matematiki 3 Russian Physics Journal 3 Multiscale Modeling & Simulation 3 Annali della Scuola Normale Superiore di Pisa. Scienze Fisiche e Matematiche. III. Ser 2 Applicable Analysis 2 Computers & Mathematics with Applications 2 Journal d’Analyse Mathématique 2 Journal of Engineering Mathematics 2 Journal of Differential Equations 2 Journal of Scientific Computing 2 Computational Mathematics and Mathematical Physics 2 Journal de Mathématiques Pures et Appliquées. Neuvième Série 2 SIAM Journal on Applied Mathematics 2 Integral Transforms and Special Functions 2 Doklady Mathematics 2 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 1 Acta Mechanica 1 Computer Physics Communications 1 Communications on Pure and Applied Mathematics 1 International Journal of Engineering Science 1 Journal of Fluid Mechanics 1 Journal of Mathematical Biology 1 Lithuanian Mathematical Journal 1 Mathematical Methods in the Applied Sciences 1 Physics Letters. A 1 Russian Mathematical Surveys 1 Ukrainian Mathematical Journal 1 ZAMP. Zeitschrift für angewandte Mathematik und Physik 1 Zhurnal Vychislitel’noĭ Matematiki i Matematicheskoĭ Fiziki 1 Mathematics of Computation 1 Acta Mathematica 1 Inventiones Mathematicae 1 Journal für die Reine und Angewandte Mathematik 1 Kodai Mathematical Journal 1 Mathematische Annalen 1 Numerische Mathematik 1 Publications of the Research Institute for Mathematical Sciences, Kyoto University 1 Transactions of the American Mathematical Society 1 Transactions of the Moscow Mathematical Society 1 Optimal Control Applications & Methods 1 Physica D 1 European Journal of Applied Mathematics 1 Computational Mathematics and Modeling 1 Communications in Partial Differential Equations 1 SIAM Journal on Mathematical Analysis 1 Vestnik St. Petersburg University. Mathematics 1 SIAM Journal on Scientific Computing 1 Izvestiya: Mathematics 1 Differential Equations and Dynamical Systems 1 Journal of Applied Mechanics and Technical Physics 1 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Regular and Chaotic Dynamics 1 Journal of Nonlinear Mathematical Physics 1 Differential Equations 1 Matematicheskoe Modelirovanie 1 Archives of Computational Methods in Engineering 1 Vestnik Novosibirskogo Gosudarstvennogo Universiteta. Seriya: Matematika, Mekhanika, Informatika 1 Journal of the Institute of Mathematics of Jussieu 1 Sibirskie Èlektronnye Matematicheskie Izvestiya 1 PMM, Journal of Applied Mathematics and Mechanics 1 Complex Variables and Elliptic Equations 1 Journal of $$K$$-Theory 1 Science China. Mathematics 1 Ufimskiĭ Matematicheskiĭ Zhurnal 1 Forum of Mathematics, Pi 1 Nonlinear Analysis. Theory, Methods & Applications 1 Research in the Mathematical Sciences 1 Philosophical Transactions of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 1 Pure and Applied Analysis 1 Mechanics of Solids 1 Annales Fennici Mathematici
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### Cited in 43 Fields

 227 Partial differential equations (35-XX) 104 Mechanics of deformable solids (74-XX) 78 Fluid mechanics (76-XX) 70 Optics, electromagnetic theory (78-XX) 36 Quantum theory (81-XX) 28 Numerical analysis (65-XX) 20 Global analysis, analysis on manifolds (58-XX) 17 Dynamical systems and ergodic theory (37-XX) 17 Operator theory (47-XX) 15 Ordinary differential equations (34-XX) 12 Special functions (33-XX) 12 Differential geometry (53-XX) 12 Geophysics (86-XX) 9 Mechanics of particles and systems (70-XX) 9 Statistical mechanics, structure of matter (82-XX) 8 Functional analysis (46-XX) 7 Integral equations (45-XX) 7 Systems theory; control (93-XX) 6 Approximations and expansions (41-XX) 3 History and biography (01-XX) 3 Functions of a complex variable (30-XX) 3 Biology and other natural sciences (92-XX) 2 Combinatorics (05-XX) 2 Real functions (26-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Difference and functional equations (39-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 2 Probability theory and stochastic processes (60-XX) 2 Computer science (68-XX) 1 General and overarching topics; collections (00-XX) 1 Number theory (11-XX) 1 Algebraic geometry (14-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Group theory and generalizations (20-XX) 1 Topological groups, Lie groups (22-XX) 1 Measure and integration (28-XX) 1 Potential theory (31-XX) 1 Abstract harmonic analysis (43-XX) 1 General topology (54-XX) 1 Manifolds and cell complexes (57-XX) 1 Relativity and gravitational theory (83-XX) 1 Information and communication theory, circuits (94-XX)

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