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Identifying the space source term problem for time-space-fractional diffusion equation
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DOI：10.1186/s13662-020-02998-y.png)
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Abstract
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In this paper, we consider an inverse source problem for the time-space-fractional diffusion equation. Here, in the sense of Hadamard, we prove that the problem is severely ill-posed. By applying the quasi-reversibility regularization method, we propose by this method to solve the problem (1.1). After that, we give an error estimate between the sought solution and regularized solution under a prior parameter choice rule and a posterior parameter choice rule, respectively. Finally, we present a numerical example to find that the proposed method works well.
Keywords:
Inverse source problem
Time-space-fractional diffusion equation
Ill-posed problem
Convergence estimates
Regularization method
35K05
35K99
47J06
47H10x
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