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.

中文翻译：

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三阶Moore-Gibson-Thompson方程中的卷积核确定问题

摘要

本文主要研究三阶 Moore-Gibson-Thompson (MGT) 方程中 Volterra 型积分项函数的差分核的反演问题。首先，将初始边值问题简化为等价问题。使用傅里叶谱方法，等效问题被简化为积分方程组。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该等价问题的唯一解。基于问题的等价性，证明了原反问题经典解的存在唯一性定理。