Backward problem for time fractional reaction-diffusion equation with\n nonlinear source and discrete data

2019/10/30 by Nguyen Huy Tuan, Tran Ngoc Thach, Tuan, Nguyen Huy +5 · 2 citations
Mathematics · #Fractional Differential Equations Solutions #Nonlinear Differential Equations Analysis #Differential Equations and Numerical Methods

paper · pdf · doi:10.48550/arxiv.1910.14204

Abstract

In this paper, we study the problem of finding the solution of a\nmulti-dimensional time fractional reactiondiffusion equation with nonlinear\nsource from the final value data. We prove that the present problem is not\nwell-posed. Then regularized problems are constructed using the truncated\nexpansion method (in the case of two-dimensional) and the quasi-boundary value\nmethod (in the case of multi-dimensional). Finally, convergence rates of the\nregularized solutions are given and investigated numerically.\n

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• Backward problems in time for fractional diffusion-wave equation
• Well-posedness for the backward problems in time for general time-fractional diffusion equation

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