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arXiv · 2003.13919

Numerical schemes for reconstructing profiles of moving sources in (time-fractional) evolution equations

Yikan Liu
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Abstract

This article is concerned with the derivation of numerical reconstruction schemes for the inverse moving source problem on determining source profiles in (time-fractional) evolution equations. As a continuation of the theoretical result on the uniqueness, we adopt a minimization procedure with regularization to construct iterative thresholding schemes for the reduced backward problems on recovering one or two unknown initial value(s). Moreover, an elliptic approach is proposed to solve a convection equation in the case of two profiles.

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Yikan Liu. 2020-03-31. Numerical schemes for reconstructing profiles of moving sources in (time-fractional) evolution equations. https://arxiv.org/abs/2003.13919

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