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Eurasian Journal of Mathematical and Computer Applications, 2016, том 4, выпуск 1, страницы 32–46
(Mi ejmca36)
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A problem of recovering a special two dimension potential in a hyperbolic equation
V. G. Romanov Sobolev Institute of Mathematics, Novosibirsk 630090, Koptyug prosp., 4, Russia
Аннотация:
We consider an inverse problem for partial differential equations of the second order related to recovering a coefficient (potential) in the lower term of this equations. It is supposed that the unknown potential is a trigonometric polynomial with respect to one of space variables with continuous coefficients of the other variable. The direct problem for the hyperbolic equation is the initial-boundary value problem for half-space $x > 0$ with zero initial Cauchy data and a special Neumann data at $x = 0$. We prove a local existence theorem for the inverse problem. The used method gives stability estimates for the solution to the direct and inverse problems and proposes a method of solving them.
Ключевые слова:
inverse problem, hyperbolic equation, uniqueness, existence.
Поступила в редакцию: 10.02.2016
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Страница аннотации: | 72 |
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