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Final value problem for nonlinear time fractional reaction-diffusion equation with discrete data. (English) Zbl 1436.35327

Summary: In this paper, we study the problem of finding the solution of a multi-dimensional time fractional reaction-diffusion equation with nonlinear source from the final value data. We prove that the present problem is not well-posed. Then regularized problems are constructed using the truncated expansion method (in the case of two-dimensional) and the quasi-boundary value method (in the case of multi-dimensional). Finally, convergence rates of the regularized solutions are given and investigated numerically.

MSC:

35R30 Inverse problems for PDEs
65M32 Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs
35K20 Initial-boundary value problems for second-order parabolic equations
35R11 Fractional partial differential equations
47H10 Fixed-point theorems
47J06 Nonlinear ill-posed problems
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