Optimization method for the inverse problem of reconstructing the source term in a parabolic equation

Authors:
Liu Yang;Zui-Cha Deng;Jian-Ning Yu;Guan-Wei Luo
Affiliations:
Department of Mathematics, Lanzhou Jiaotong University, Lanzhou, Gansu 730070, People's Republic of China;Department of Mathematics, Lanzhou Jiaotong University, Lanzhou, Gansu 730070, People's Republic of China;Department of Mathematics, Lanzhou Jiaotong University, Lanzhou, Gansu 730070, People's Republic of China;Department of Mathematics, Lanzhou Jiaotong University, Lanzhou, Gansu 730070, People's Republic of China
Venue:
Mathematics and Computers in Simulation
Year:
2009

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Abstract

This work investigates the inverse problem of reconstructing a spacewise dependent heat source in the parabolic heat equation using a final temperature measurement. Such problem has important application in a large field of applied science. On the basis of the optimal control framework, the existence and necessary condition of the minimizer for the cost functional are established. The global uniqueness and stability of the minimizer are deduced from the necessary condition. The Landweber iteration algorithm is applied to the inverse problem and some numerical results are presented for various typical test examples.