Determination of Compactly Supported Sources for the One-Dimensional Heat Equation

被引：0

作者：

Solov'ev, V. V. ^{[1
]}

机构：

[1] Natl Res Nucl Univ MEPhI, Moscow 115409, Russia

来源：

COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS | 2020年 / 60卷 / 09期

关键词：

heat equation; unknown source; inverse problem; uniqueness of solution; existence of solution;

D O I：

10.1134/S0965542520090146

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The inverse problem of determining a source in the one-dimensional heat equation in the case of a Dirichlet boundary value problem is investigated. The trace of the solution of the direct problem on straight-line segments inside the domain at the final time is specified as overdetermination (i.e., additional information on the solution of the direct problem). A Fredholm alternative theorem for this problem is proved, and sufficient conditions for its unique solvability are obtained. The inverse problem is considered in classes of smooth functions with derivatives satisfying the Holder condition.

引用

页码：1555 / 1569

页数：15

共 15 条

[1]

[Anonymous], 1989, DIFFER EQU

[2]

[Anonymous], 2000, Methods for solving inverse problems in mathematical physics

[3] Problems of determining the unknown source in parabolic and hyperbolic equations [J].