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An Inverse Source Problem with Sparsity Constraint for the Time-Fractional Diffusion Equation

An Inverse Source Problem with Sparsity Constraint for the Time-Fractional Diffusion Equation
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Year:    2016

Author:    Zhousheng Ruan, Zhijian Yang, Xiliang Lu

Advances in Applied Mathematics and Mechanics, Vol. 8 (2016), Iss. 1 : pp. 1–18

Abstract

In this paper, an inverse source problem for the time-fractional diffusion equation is investigated. The observational data is on the final time and the source term is assumed to be temporally independent and with a sparse structure. Here the sparsity is understood with respect to the pixel basis, i.e., the source has a small support. By an elastic-net regularization method, this inverse source problem is formulated into an optimization problem and a semismooth Newton (SSN) algorithm is developed to solve it. A discretization strategy is applied in the numerical realization. Several one- and two- dimensional numerical examples illustrate the efficiency of the proposed method.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aamm.2014.m722

Advances in Applied Mathematics and Mechanics, Vol. 8 (2016), Iss. 1 : pp. 1–18

Published online:    2016-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    18

Keywords:   

Author Details

Zhousheng Ruan

Zhijian Yang

Xiliang Lu

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