Convolution Kernel Determination Problem in the Third Order Moore–Gibson–Thompson Equation

IF 0.5 Q3 MATHEMATICS

Russian Mathematics Pub Date : 2024-02-28 DOI:10.3103/s1066369x23120034

D. K. Durdiev, A. A. Boltaev, A. A. Rahmonov

引用次数: 0

Abstract

This article is concerned with the study of the inverse problem of determining the difference kernel in a Volterra type integral term function in the third-order Moore–Gibson–Thompson (MGT) equation. First, the initial-boundary value problem is reduced to an equivalent problem. Using the Fourier spectral method, the equivalent problem is reduced to a system of integral equations. The existence and uniqueness of the solution to the integral equations are proved. The obtained solution to the integral equations of Volterra-type is also the unique solution to the equivalent problem. Based on the equivalence of the problems, the theorem of the existence and uniqueness of the classical solutions of the original inverse problem is proved.

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三阶摩尔-吉布森-汤普森方程中的卷积核确定问题

摘要本文主要研究三阶摩尔-吉布森-汤普森（MGT）方程中 Volterra 型积分项函数的差分核的逆问题。首先，初界值问题被简化为等价问题。利用傅立叶谱方法，等效问题被简化为一个积分方程组。证明了积分方程解的存在性和唯一性。所得到的 Volterra 型积分方程的解也是等价问题的唯一解。基于问题的等价性，证明了原始逆问题经典解的存在性和唯一性定理。

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

Russian Mathematics MATHEMATICS-

CiteScore

0.90

自引率

25.00%

发文量

期刊介绍： Russian Mathematics is a peer reviewed periodical that encompasses the most significant research in both pure and applied mathematics.