Abstract: A quasilinear hyperbolic equation is considered whose principal part is a purely wave operator and the lower order part consists of two nonlinear terms with coefficients and compactly supported in a ball . We study the direct problem of a plane wave scattered by a heterogeneity localized in and the inverse problem of recovering the coefficients and from solutions of direct problems with a varying incident wave direction. An asymptotic expansion of the solution to the direct problem near the front of the traveling plane wave is presented, based on which the inverse problem is reduced to two linear problems to be solved sequentially. Namely, the problem of determining the coefficient is reduced to a classical X-ray tomography problem, while the problem of determining the coefficient is reduced to a more complicated problem of integral geometry. The last problem, which is new, is to find a function from its integrals with a given weight along straight lines. This problem is investigated, and a uniqueness and stability theorem for its solution is proved.

Cite: Romanov V.G.
Inverse Problem for a Quasilinear Wave Equation
Computational Mathematics and Mathematical Physics. 2025. V.65. N6. P.1344-1353. DOI: 10.1134/s096554252570040x WOS Scopus РИНЦ OpenAlex

Original: Романов В.Г.
Обратная задача для квазилинейного волнового уравнения
Журнал вычислительной математики и математической физики. 2025. Т.65. №6. С.961-971. DOI: 10.31857/S0044466925060093 РИНЦ

Dates:

Submitted:	Nov 28, 2024
Accepted:	Mar 27, 2025
Published print:	Aug 6, 2025
Published online:	Aug 6, 2025

Identifiers:

Web of science:	WOS:001551465700017
Scopus:	2-s2.0-105012775128
Elibrary:	82714642
OpenAlex:	W4413049500

Citing: Пока нет цитирований

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