On a backward problem for nonlinear fractional diffusion equations

Authors: Nguyễn Huy Tuấn, Lê Nhật Huynh, Tran Bao Ngoc, Yong Zhou, Nguyễn Huy Tuấn,

https://doi.org/10.1016/j.aml.2018.11.015

Publisher, magazine: ,

Publication year: 2019

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Abstract

In this paper, a backward problem for a time–space fractional diffusion with nonlinear source has been considered. Under some assumptions, we establish the existence and uniqueness of mild solutions of a local solution to the nonlinear problem. We also prove that our backward problem is ill-posed in the sense of Hadamard. A regularization method has been proposed to approximate the solution. Furthermore, the convergence rate for the regularized solution can be proved.

Tags: Backward problem, Regularization, Fractional diffusion equation, Fixed point theory