AN INVERSE PROBLEM FOR THE WAVE EQUATION WITH TWO NONLINEAR TERMS

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详细

An inverse problem for a hyperbolic equation of the second order containing two nonlinear terms is studied. It consists in recovering coefficients under nonlinearities. The Cauchy problem with a point source located at point y is considered. This point is a parameter of the problem and runs an spherical surface ???? successively. It is supposed that unknown coefficients are differed from zero in domain be situated inside of ???? only. The trace of a solution of the Cauchy problem is given on ???? for all values of y and for all times closed to moments of arriving of the wave from y to points of ????. It is proved that this information allows to reduce the inverse problem to two problems of the integral geometry solving successively. For latter problems stability estimates are stated.

作者简介

V. Romanov

Sobolev Institute of Mathematics SB RAS

Email: romanov@math.nsc.ru
Novosibirsk, Russia

参考

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