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

Autor:	V. V. Solov’ev
Rok vydání:	2020
Předmět:	Computational Mathematics symbols.namesake Trace (linear algebra) Mathematical analysis symbols Hölder condition Heat equation Boundary value problem Inverse problem Fredholm alternative Domain (mathematical analysis) Dirichlet distribution Mathematics
Zdroj:	Computational Mathematics and Mathematical Physics. 60:1555-1569
ISSN:	1555-6662 0965-5425
Popis:	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.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::5a356f1bdb3158113b05d95399f61e90 https://doi.org/10.1134/s0965542520090146 Zobrazit plný text záznamu Full text from SpringerLink