An inverse source problem in a semilinear time-fractional diffusion equation

被引：26
|
作者：
Slodicka, M. [1 ]
Siskova, K. [1 ]
机构：
[1] Univ Ghent, Dept Math Anal, Res Grp Numer Anal & Math Modeling NaM2, Galglaan 2 S22, B-9000 Ghent, Belgium
来源：
COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2016年 / 72卷 / 06期
关键词：
Semilinear time-fractional diffusion; equation; Inverse source problem; Reconstruction; Convergence; Time discretization; SOURCE-TERM; HEAT-SOURCE; UNIQUENESS;
D O I：
10.1016/j.camwa.2016.07.029
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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.
引用
收藏
页码：1655 / 1669
页数：15
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