Approximation of the Solution of an Inverse Problem for a Singularly Perturbed System of Partial Differential Equations

We consider an initial–boundary value problem for a singularly perturbed system of partial differential equations. We pose an inverse problem of determining an unknown initial condition based on additional information about the solution of the initial–boundary value problem. It is proved that using...

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Bibliographic Details
Published inDifferential equations Vol. 59; no. 6; pp. 762 - 768
Main Author Denisov, A. M.
Format Journal Article
LanguageEnglish
Published Moscow Pleiades Publishing 01.06.2023
Springer
Springer Nature B.V
Subjects
Approximation
Boundary value problems
Difference and Functional Equations
Differential equations
Inverse problems
Mathematical analysis
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
Partial Differential Equations
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Summary:We consider an initial–boundary value problem for a singularly perturbed system of partial differential equations. We pose an inverse problem of determining an unknown initial condition based on additional information about the solution of the initial–boundary value problem. It is proved that using the expansion of the solution of the initial–boundary value problem in the small parameter , one can obtain solutions approximating the solution of the inverse problem with order or .
ISSN:0012-2661
1608-3083
DOI:10.1134/S0012266123060058