A new regularization method for solving a time-fractional inverse diffusion problem. (English) Zbl 1211.35281
Summary: We consider an inverse problem for a time-fractional diffusion equation in a one-dimensional semi-infinite domain. The temperature and heat flux are sought from a measured temperature history at a fixed location inside the body. We show that such problem is severely ill-posed and further apply a new regularization method to solve it based on the solution given by the Fourier method. Convergence estimates are presented under the a priori bound assumptions for the exact solution. Finally, numerical examples are given to show that the proposed numerical method is effective.
MSC:
| 35R30 | Inverse problems for PDEs |
| 35R11 | Fractional partial differential equations |
| 80A23 | Inverse problems in thermodynamics and heat transfer |
| 65M32 | Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs |
| 26A33 | Fractional derivatives and integrals |
| 35A22 | Transform methods (e.g., integral transforms) applied to PDEs |
| 65T50 | Numerical methods for discrete and fast Fourier transforms |
Keywords:
regularization method; Caputo’s fractional derivatives; temperature; heat flux; Fourier transform; Laplace transformReferences:
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