Inverse problems for a generalized subdiffusion equation with final overdetermination

We consider two inverse problems for a generalized subdiffusion equation that use the final overdetermination condition. Firstly, we study a problem of reconstruction of a specific space-dependent component in a source term. We prove existence, uniqueness and stability of the solution to this proble...

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Bibliographic Details
Published inMathematical modelling and analysis Vol. 24; no. 2; pp. 236 - 262
Main Authors Kinash, Nataliia, Janno, Jaan
Format Journal Article
LanguageEnglish
Published Vilnius Vilnius Gediminas Technical University 18.03.2019
Subjects
final overdetermination
fractional diffusion
Heat equation
Inverse functions
inverse problem
Inverse problems
Mathematical research
Stability
subdiffusion
Uniqueness
inverse problem
subdiffusion
final overdetermination
fractional diffusion
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Summary:We consider two inverse problems for a generalized subdiffusion equation that use the final overdetermination condition. Firstly, we study a problem of reconstruction of a specific space-dependent component in a source term. We prove existence, uniqueness and stability of the solution to this problem. Based on these results, we consider an inverse problem of identification of a space-dependent coefficient of a linear reaction term. We prove the uniqueness and local existence and stability of the solution to this problem.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1392-6292
1648-3510
DOI:10.3846/mma.2019.016