Name: ON SOME CLASSES OF INVERSE PARABOLIC PROBLEMS OF RECOVERING THE THERMOPHYSICAL PARAMETERS
Keywords: Inverse problems for PDEs, parabolic equation, Initial-boundary value problems for second-order parabolic equations, обратная задача, единственность, УДК 517.956, existence, inverse problem, uniqueness, начально-краевая задача

О НЕКОТОРЫХ КЛАССАХ ОБРАТНЫХ ПАРАБОЛИЧЕСКИХ ЗАДАЧ ВОССТАНОВЛЕНИЯ ТЕРМОФИЗИЧЕСКИХ ПАРАМЕТРОВ

descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 2023Publisher:FSAEIHE South Ural State University (National Research University)Journal:Bulletin of the South Ural State University series "Mathematics. Mechanics. Physics", volume 15, pages 23-33 (issn: 2075-809X, eissn: 2409-6547,

Authors: S.G. Pyatkov; O.A. Soldatov;

doi: 10.14529/mmph230303

ON SOME CLASSES OF INVERSE PARABOLIC PROBLEMS OF RECOVERING THE THERMOPHYSICAL PARAMETERS

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Abstract

In the article we examine the question of regular solvability in Sobolev spaces of parabolic inverse coefficient problems. A solution is sought in the class of regular solutions that has all derivatives occurring in the equation summable to some power. The overdetermination conditions are the values of a solution at some collection of points lying inside the domain. The proof is based on a priori estimates and the fixed point theorem.

Related Organizations

South Ural State University (Южно-Уральский государственный университет)
Russian Federation
Yugra State University
Russian Federation

Keywords

Inverse problems for PDEs, parabolic equation, Initial-boundary value problems for second-order parabolic equations, обратная задача, единственность, УДК 517.956, existence, inverse problem, uniqueness, начально-краевая задача, существование, initial-boundary value problem, параболическое уравнение

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