The Inverse Problem for a Quasilinear Wave Equation with Memory

The Inverse Problem for a Quasilinear Wave Equation with Memory Full article

Journal

Journal of Applied and Industrial Mathematics
ISSN: 1990-4789 , E-ISSN: 1990-4797

Output data

Year: 2025, Volume: 19, Number: 1, Pages: 104-130 Pages count : 27 DOI: 10.1134/S1990478925010107

Funding (1)

Sobolev Institute of Mathematics

FWNF-2022-0009

The forward and inverse problems are investigated for the quasilinear wave equation □u−q(x)u2−K∗u=0 where the kernel K(x,t) is represented in the form K(x,t)=p(x)K0(t) with p(x) being a continuous function. The inverse problem is devoted to the determination of the compact functions q(x) and p(x). Traces of the derivative with respect to x of two solutions to the forward initial–boundary value problem related to two arbitrary boundary data are given for x=0 on the finite segment [0,T] as an additional information for the solution to the inverse problem. The conditions for the unique solvability of the forward problem are found. A local existence and uniqueness theorem is proved for the inverse problem.

Romanov V.G. , Bugueva T.V.
The Inverse Problem for a Quasilinear Wave Equation with Memory
Journal of Applied and Industrial Mathematics. 2025. V.19. N1. P.104-130. DOI: 10.1134/S1990478925010107 Scopus РИНЦ

Романов В.Г. , Бугуева Т.В.
Обратная задача для квазилинейного волнового уравнения с памятью
Сибирский журнал индустриальной математики. 2025. Т.28. №1. С.38-66. DOI: 10.33048/SIBJIM.2025.28.104 РИНЦ

Submitted:	Nov 22, 2024
Accepted:	Mar 10, 2025
Published print:	Nov 2, 2025
Published online:	Nov 2, 2025

Scopus:	2-s2.0-105020677592
Elibrary:	83155455

Пока нет цитирований