M. M. Lavrentiev积分方程解的唯一性条件及数值逼近

IF 0.4 Q4 MATHEMATICS, APPLIED Numerical Analysis and Applications Pub Date : 2022-12-01 DOI:10.15372/sjnm20220409

M. Kokurin, V. V. Klyuchev

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引用次数: 0

摘要

m.m.l avrentiev线性积分方程是由非线性系数反波传感问题的一种特殊变换而产生的。证明了正则调和函数与牛顿势由段支持的积集的完备性。作为推论，我们建立了m.m.l avrentiev方程解的唯一性和相关的波传感反问题。我们用并行计算给出了这个方程的近似解的结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Uniqueness Conditions and Numerical Approximation of the Solution to M. M. Lavrentiev’s Integral Equation

Abstract M.M. Lavrentiev’s linear integral equation arises as a result of a special transformation of a nonlinear coefficient inverse wave sensing problem. The completeness of the set of products of regular harmonic functions and Newtonian potentials supported by a segment is proved. As a corollary, we establish the uniqueness of the solution to M.M. Lavrentiev’s equation and a related inverse problem of wave sensing. We present results of an approximate solution of this equation by using parallel calculations.

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来源期刊

Numerical Analysis and Applications MATHEMATICS, APPLIED-

CiteScore

1.00

自引率

0.00%

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期刊介绍： Numerical Analysis and Applications is the translation of Russian periodical Sibirskii Zhurnal Vychislitel’noi Matematiki (Siberian Journal of Numerical Mathematics) published by the Siberian Branch of the Russian Academy of Sciences Publishing House since 1998. The aim of this journal is to demonstrate, in concentrated form, to the Russian and International Mathematical Community the latest and most important investigations of Siberian numerical mathematicians in various scientific and engineering fields. The journal deals with the following topics: Theory and practice of computational methods, mathematical physics, and other applied fields; Mathematical models of elasticity theory, hydrodynamics, gas dynamics, and geophysics; Parallelizing of algorithms; Models and methods of bioinformatics.