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Inverse source problem for a fractional diffusion equation. (English) Zbl 1211.35280

Summary: An inverse source problem for a fractional diffusion equation is investigated. Under an assumption that the unknown source term is time independent, an analytical solution can be deduced based on the method of the eigenfunction expansion. Then, the uniqueness of the inverse problem is proved by analytic continuation and Laplace transform. Regularization schemes are considered to obtain the regularized solution. Numerical examples are presented to illustrate the validity and effectiveness of the proposed meshless method.

MSC:

35R30 Inverse problems for PDEs
35R11 Fractional partial differential equations
35A22 Transform methods (e.g., integral transforms) applied to PDEs
65M32 Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs
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