Abstract: For the wave equation with two nonlinear terms we consider the inverse problem consisting in recovering finitely supported coefficients of the nonlinear terms by using an information about the solutions corresponding to the plane waves coming from infinity and passing through inhomogeneity. The direction of propagation of plane waves is considered as a parameter of the problem, and the solution is measured at the boundary of the domain the interior of which contains the support of the unknown coefficients at time moments close to the arrival time of the wave front. The main result is that we reduce the inverse problem to the usual X-ray tomography problem for one of the coefficients at the nonlinear terms and a new integral geometry problem for the other coefficient. For the latter problem we derive the stability estimate for solutions.

Cite: Romanov V.G.
Inverse Problem for Quasilinear Wave Equation
Journal of Mathematical Sciences (United States). 2024. V.284. N1. P.140-148. DOI: 10.1007/s10958-024-07332-5 Scopus РИНЦ OpenAlex

Original: Романов В.Г.
Обратная задача для квазилинейного волнового уравнения
Сириус. Математический журнал. 2024. Т.1. №1. С.105-112.

Dates:

Accepted:	Mar 25, 2024
Submitted:	Apr 7, 2024
Published print:	Aug 19, 2024
Published online:	Aug 19, 2024

Identifiers:

Scopus:	2-s2.0-85201548030
Elibrary:	73649458
OpenAlex:	W4401710081

Citing:

DB	Citing
OpenAlex	1

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