VARIATIONAL METHOD FOR A BACKWARD PROBLEM FOR A TIME-FRACTIONAL DIFFUSION EQUATION

被引：8

作者：

Wei, Ting ^{[1
]}

Xian, Jun ^{[1
]}

机构：

[1] Lanzhou Univ, Sch Math & Stat, Lanzhou 730000, Gansu, Peoples R China

来源：

ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE | 2019年 / 53卷 / 04期

关键词：

Backward problem; fractional diffusion equation; Tikhonov regularization; variational method; conjugate gradient method; DIFFERENCE APPROXIMATION; COEFFICIENT; TRANSPORT;

D O I：

10.1051/m2an/2019019

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is devoted to solve a backward problem for a time-fractional diffusion equation by a variational method. The regularity of a weak solution for the direct problem as well as the existence and uniqueness of a weak solution for the adjoint problem are proved. We formulate the backward problem into a variational problem by using the Tikhonov regularization method, and obtain an approximation to the minimizer of the variational problem by using a conjugate gradient method. Four numerical examples in one-dimensional and two-dimensional cases are provided to show the effectiveness of the proposed algorithm.

引用

页码：1223 / 1244

页数：22

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