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Journal of Applied and Industrial Mathematics

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01-05-2022

Inverse Problem for a Nonlinear Wave Equation

Authors: V. G. Romanov, T. V. Bugueva

Published in: Journal of Applied and Industrial Mathematics | Issue 2/2022

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Abstract

We consider the inverse problem of determining the coefficient of the nonlinear term in an equation whose main part is the wave operator. The properties of the solution of the direct problem are studied; in particular, the existence and uniqueness of a bounded solution in a neighborhood of the characteristic cone is established, and the structure of this solution is written out. The problem of finding the unknown function is reduced to the problem of integral geometry on a family of straight lines with a weight function invariant with respect to rotations around some fixed point. The uniqueness of the solution of the inverse problem is established, and an algorithm for reconstructing the desired function is proposed.

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Title: Inverse Problem for a Nonlinear Wave Equation
Authors: V. G. Romanov
T. V. Bugueva
Publication date: 01-05-2022
Publisher: Pleiades Publishing
Published in: Journal of Applied and Industrial Mathematics / Issue 2/2022
Print ISSN: 1990-4789
Electronic ISSN: 1990-4797
DOI: https://doi.org/10.1134/S1990478922020132

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