A Two Dimensional Discrete Mollification Operator and the Numerical Solution of an Inverse Source Problem

A Two Dimensional Discrete Mollification Operator and the Numerical Solution of an Inverse Source Problem

We consider a two-dimensional time fractional diffusion equation and address the important inverse problem consisting of the identification of an ingredient in the source term. The fractional derivative is in the sense of Caputo. The necessary regularization procedure is provided by a two-dimensiona...

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Veröffentlicht in:Axioms 2018-11, Vol.7 (4), p.89
Hauptverfasser: Echeverry, Manuel, Mejía, Carlos
Format: Artikel
Sprache:eng
Schlagworte:
Boundary value problems
fractional derivatives
inverse problem
Inverse problems
mollification
Regularization
Regularization methods
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Beschreibung
Zusammenfassung:We consider a two-dimensional time fractional diffusion equation and address the important inverse problem consisting of the identification of an ingredient in the source term. The fractional derivative is in the sense of Caputo. The necessary regularization procedure is provided by a two-dimensional discrete mollification operator. Convergence results and illustrative numerical examples are included.
ISSN:2075-1680
2075-1680
DOI:10.3390/axioms7040089