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Zbl 1183.65118
Yang, Liu; Deng, Zui-Cha; Yu, Jian-Ning; Luo, Guan-Wei
Optimization method for the inverse problem of reconstructing the source term in a parabolic equation. (English)
[J] Math. Comput. Simul. 80, No. 2, 314-326 (2009). ISSN 0378-4754

The authors consider an inverse problem of reconstructing in the parabolic heat equation a heat source term which depends on the spatial variable using a final temperature measurement. The authors use an optimal control framework to discuss this problem. The existence and a necessary condition of the minimizer for the cost functional are established. The global uniqueness and stability of the minimizer for the cost functional are proved. The Landweber iteration algorithm is applied to the inverse problem and some numerical results are also presented.
[Damian Słota (Gliwice)]

MSC 2000:: *65M32 Inverse problems
35R30 Inverse problems for PDE
49J20 Optimal control problems with PDE (existence)
35Q05 Euler-Poisson-Darboux equation and generalizations
80A23 Inverse problems (thermodynamics)
65M12 Stability and convergence of numerical methods (IVP of PDE)

Keywords: inverse problem; source term; optimization method; numerical results; parabolic heat equation; optimal control; stability; Landweber iteration

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Zentralblatt MATH Berlin [Germany]