IDENTIFYING AN UNKNOWN SOURCE IN SPACE-FRACTIONAL DIFFUSION EQUATION

doi:10.1016/S0252-9602(14)60065-5

Abstract

Abstract:

In this paper, we identify a space-dependent source for a fractional diffusion equation. This problem is ill-posed, i.e., the solution (if it exists) does not depend continu-ously on the data. The generalized Tikhonov regularization method is proposed to solve this problem. An a priori error estimate between the exact solution and its regularized approxi-mation is obtained. Moreover, an a posteriori parameter choice rule is proposed and a stable error estimate is also obtained. Numerical examples are presented to illustrate the validity and effectiveness of this method.

Key words: spatial-dependent heat source, space-fractional diffusion equation, generalized Tikhonov regularization, A posteriori parameter choice, error estimate

CLC Number:

35R30

YANG Fan, FU Chu-Li, LI Xiao-Xiao. IDENTIFYING AN UNKNOWN SOURCE IN SPACE-FRACTIONAL DIFFUSION EQUATION[J].Acta mathematica scientia,Series B, 2014, 34(4): 1012-1024.

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