AN INVERSE PROBLEM FOR A NONLINEAR WAVE EQUATION WITH DAMPING

IF 0.6 Q4 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Eurasian Journal of Mathematical and Computer Applications Pub Date : 2023-01-01 DOI:10.32523/2306-6172-2023-11-2-99-115

V. Romanov

引用次数: 0

Abstract

We consider an inverse problem of recovering two coefficients in a semi-linear wave equation. This equation contains a damping term and a term with a quadratic nonlinearity. The inverse problem consists in recovering coefficients under these terms as function of the space variable x ∈ R 3 . A forward problem for the equation with a point source is studied. As a result, the inverse problem reduce to two problems, one of them is the well known problem of X-ray tomography, the other one is the problem of the integral geometry with a with a special weight function. The latter problem is studied and a stability estimate for the solution of this problem is stated.

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带阻尼的非线性波动方程的反问题

考虑半线性波动方程中两个系数的反演问题。该方程包含一个阻尼项和一个二次非线性项。逆问题包括在这些项下恢复系数作为空间变量x∈r3的函数。研究了带点源方程的正演问题。将反问题简化为两个问题，一个是众所周知的x射线层析成像问题，另一个是带有特殊权函数的几何积分问题。对后一个问题进行了研究，并给出了该问题解的稳定性估计。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Eurasian Journal of Mathematical and Computer Applications MATHEMATICS, INTERDISCIPLINARY APPLICATIONS-

CiteScore

1.40

自引率

0.00%

发文量

期刊介绍： Eurasian Journal of Mathematical and Computer Applications (EJMCA) publishes carefully selected original research papers in all areas of Applied mathematics first of all from Europe and Asia. However papers by mathematicians from other continents are also welcome. From time to time Eurasian Journal of Mathematical and Computer Applications (EJMCA) will also publish survey papers. Eurasian Mathematical Journal publishes 4 issues in a year. A working language of the journal is English. Main topics are: - Mathematical methods and modeling in mechanics, mining, biology, geophysics, electrodynamics, acoustics, industry. - Inverse problems of mathematical physics: theory and computational approaches. - Medical and industry tomography. - Computer applications: distributed information systems, decision-making systems, embedded systems, information security, graphics.