n 维空间中拉夫伦特埃夫积分方程解法的唯一性

IF 0.7 4区数学 Q3 MATHEMATICS, APPLIED

Computational Mathematics and Mathematical Physics Pub Date : 2024-04-22 DOI:10.1134/s0965542524030084

M. M. Kokurin, V. V. Klyuchev, A. V. Gavrilova

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引用次数: 0

摘要

摘要我们研究了 Lavrent'ev 积分方程的多维类似方程，并将声学探测的反问题简化为该方程。确定了所研究方程具有唯一解的条件。文中还介绍了在声源和探测器位置各异的情况下解决反声学问题的数值实验结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Uniqueness of a Solution to the Lavrent’ev Integral Equation in n-Dimensional Space

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Uniqueness of a Solution to the Lavrent’ev Integral Equation in n-Dimensional Space

Abstract

We study the multidimensional analogue of the Lavrent’ev integral equation to which an inverse problem of acoustic sounding is reduced. Conditions under which the studied equation has a unique solution are established. Results of numerical experiments concerning the solution of the inverse acoustic problem with variously located sets of sources and detectors are presented.

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来源期刊

Computational Mathematics and Mathematical Physics MATHEMATICS, APPLIED-PHYSICS, MATHEMATICAL

CiteScore

1.50

自引率

14.30%

发文量

125

审稿时长

4-8 weeks

期刊介绍： Computational Mathematics and Mathematical Physics is a monthly journal published in collaboration with the Russian Academy of Sciences. The journal includes reviews and original papers on computational mathematics, computational methods of mathematical physics, informatics, and other mathematical sciences. The journal welcomes reviews and original articles from all countries in the English or Russian language.