Journal
JOURNAL OF INVERSE AND ILL-POSED PROBLEMS
Volume 28, Issue 1, Pages 17-32Publisher
WALTER DE GRUYTER GMBH
DOI: 10.1515/jiip-2019-0006
Keywords
Inverse source problem; distributed-order time fractional diffusion equation; Tikhonov regularization; convergence analysis; a-priori parameter choice; Morozov's discrepancy principle
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This paper studies an inverse source problem for a time fractional diffusion equation with the distributed order Caputo derivative. The space-dependent source term is recovered from a noisy final data. The uniqueness, ill-posedness and a conditional stability for this inverse source problem are obtained. The inverse problem is formulated into a minimization functional with Tikhonov regularization method. Further, based on the series representation of the regularized solution, we give convergence rates of the regularized solution under an a-priori and an a-posteriori regularization parameter choice rule. With an adjoint technique for computing the gradient of the regularization functional, the conjugate gradient method is applied to reconstruct the space-dependent source term. Two numerical examples illustrate the effectiveness of the proposed method.
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