Final value problem for nonlinear time fractional reaction–diffusion equation with discrete data

Authors: Nguyễn Huy Tuấn, Trần Ngọc Thạch, Donal O'Regan, Nguyễn Hữu Cần, Dumitru Baleanu, Nguyễn Huy Tuấn, Donal O’Regan,

https://doi.org/10.1016/j.cam.2020.112883

Publisher, magazine: ,

Publication year: 2020

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Abstract

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.

Tags: Backward problem, Fractional reaction–diffusion equation, Regularization method, Nonlinear source, Discrete data