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193 results on '"Levenshtam, V."'

4. ASYMPTOTIC PROBLEMS OF RECONSTRUCTION OF HIGH-FREQUENCY DATA OF THE WAVE EQUATION

Author

Korablina, E. V. and Levenshtam, V. B.

Subjects
Mathematics
Abstract

We consider the Cauchy problem for the one-dimensional hyperbolic equation with an unknown right-hand side, which rapidly oscillates in time. This right-hand side is the product of two functions, with one being a function of a time variable and a space variable and the other one being a function of a time variable and a so-called fast time variable. We formulate and solve four asymptotic problems of exact reconstruction of the source from certain information about the partial asymptotics of the solution., Author(s): E. V. Korablina [sup.1], V. B. Levenshtam [sup.1] [sup.2] Author Affiliations: (1) https://ror.org/01tv9ph92, grid.182798.d, 0000 0001 2172 8170, Southern Federal University, , Milchakov Street, 8A, 344058, Rostov-on-Don, Russia (2) [...]

Published
2023
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6. Inverse problems in the multidimensional hyperbolic equation with rapidly oscillating absolute term

Author

V., Babich P. and B, Levenshtam V.

Subjects
Mathematical Physics, Mathematics - Analysis of PDEs
Abstract

The paper is devoted to the development of the theory of inverse problems for evolution equations with terms rapidly oscillating in time. A new approach to setting such problems is developed for the case in which additional constraints are imposed only on several first terms of the asymptotics of the solution rather that on the whole solution. This approach is realized in the case of a multidimensional hyperbolic equation with unknown absolute term.

Published
2020

11. Recovery of a fast oscillating free term in the wave equation by asymptotics of the solution

Author

Babich, P. V. and Levenshtam, V. B.

Subjects
Mathematics - Analysis of PDEs, 35B40
Abstract

Three problems about recovery of a high-frequency free term in the one-dimension wave equation with homogeneous initial-boundary conditions by some information about partial asymptotics of its solution have been solved. It is shoun, that the free term can be completely recovered from a specific data about incomplete (three-terms) asymptotics of the solution. Before formulation of the each problem about recovery of free term, construction and justification of the asymptotics of the solution of original initial-boundary problem are given., Comment: 23 pages, in Russian

Published
2017

20. On the Averaging Method for the Problem of Heat Convection in the Field of Highly-Oscillating Forces

Author

Levenshtam, V. B., Gohberg, I., editor, Alpay, D., editor, Arazy, J., editor, Atzmon, A., editor, Ball, J. A., editor, Ben-Artzi, A., editor, Bercovici, H., editor, Böttcher, A., editor, Clancey, K., editor, Coburn, L. A., editor, Curto, R. E., editor, Davidson, K. R., editor, Douglas, R. G., editor, Dijksma, A., editor, Dym, H., editor, Fuhrmann, P. A., editor, Gramsch, B., editor, Helton, J. A., editor, Kaashoek, M. A., editor, Kaper, H. G., editor, Kuroda, S. T., editor, Lancaster, P., editor, Lerer, L. E., editor, Mityagin, B., editor, Olshevsky, V., editor, Putinar, M., editor, Rodman, L., editor, Rovnyak, J., editor, Sarason, D. E., editor, Spitkovsky, I. M., editor, Treil, S., editor, Upmeier, H., editor, Lunel, S. M. Verduyn, editor, Voiculescu, D., editor, Xia, D., editor, Yafaev, D., editor, Erusalimsky, Yakob M., editor, Gohberg, Israel, editor, Grudsky, Sergei M., editor, Rabinovich, Vladimir, editor, and Vasilevski, Nikolai, editor

Published
2007
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