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Error Estimates for the Time Discretization of a Semilinear Integrodifferential Parabolic Problem with Unknown Memory Kernel

Part of:Equations and inequalities involving nonlinear operatorsPartial differential equations, initial value and time-dependent initial-boundary value problems

Published online by Cambridge University Press:  20 February 2017

Marijke Grimmonprez,
Karel Van Bockstal and
Marián Slodička
Marijke Grimmonprez*
Affiliation:
Department of Mathematical Analysis, Ghent University, Galglaan 2, 9000 Ghent, Belgium
Karel Van Bockstal*
Affiliation:
Department of Mathematical Analysis, Ghent University, Galglaan 2, 9000 Ghent, Belgium
Marián Slodička*
Affiliation:
Department of Mathematical Analysis, Ghent University, Galglaan 2, 9000 Ghent, Belgium
*
*Corresponding author. Email addresses:marijke.grimmonprez@ugent.be (Marijke Grimmonprez), karel.vanbockstal@ugent.be (Karel Van Bockstal), marian.slodicka@ugent.be (Marián Slodička)
*Corresponding author. Email addresses:marijke.grimmonprez@ugent.be (Marijke Grimmonprez), karel.vanbockstal@ugent.be (Karel Van Bockstal), marian.slodicka@ugent.be (Marián Slodička)
*Corresponding author. Email addresses:marijke.grimmonprez@ugent.be (Marijke Grimmonprez), karel.vanbockstal@ugent.be (Karel Van Bockstal), marian.slodicka@ugent.be (Marián Slodička)

Abstract

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This paper is devoted to the study of an inverse problem containing a semilinear integrodifferential parabolic equation with an unknown memory kernel. This equation is accompanied by a Robin boundary condition. The missing kernel can be recovered from an additional global measurement in integral form. In this contribution, an error analysis is performed for a time-discrete numerical scheme based on Backward Euler's Method. The theoretical results are supported by some numerical experiments.

Keywords

Parabolic inverse problemconvolution kernelerror estimates

MSC classification

Secondary:47J35: Nonlinear evolution equations65M12: Stability and convergence of numerical methods65M32: Inverse problems

Information

Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 10 , Issue 1 , February 2017, pp. 116 - 144
Copyright
Copyright © Global-Science Press 2017 

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