Journal
COMPUTERS & MATHEMATICS WITH APPLICATIONS
Volume 72, Issue 6, Pages 1655-1669Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.camwa.2016.07.029
Keywords
Semilinear time-fractional diffusion; equation; Inverse source problem; Reconstruction; Convergence; Time discretization
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Funding
- BOF, Ghent University, Belgium [01D23414]
- Belgian Science Policy [IAP P7/02]
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We study an inverse source problem for a semilinear time-fractional diffusion equation of second order in a bounded domain in R-d. The missing solely time-dependent source is recovered from an additional integral measurement. The existence, uniqueness and regularity of a weak solution is addressed. We design a numerical algorithm based on Rothe's method, derive a priori estimates and prove convergence of iterates towards the exact solution. Theoretical results are supported by a numerical experiment. (C) 2016 Elsevier Ltd. All rights reserved.
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