Identification of an unknown source depending on both time and space variables by a variational method |
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Authors: | Yun-Jie Ma Chu-Li FuYuan-Xiang Zhang |
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Institution: | School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, PR China |
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Abstract: | The present paper is devoted to solve the problem of identifying an unknown heat source depending simultaneously on both space and time variables. This problem is transformed into an optimization problem and the uniqueness of minimum element is proved rigorously. Then a variational formulation for solving the optimization problem is given. A conjugate gradient method and a finite difference method are used to solve the variational problem. Some numerical examples are also provided to show the efficiency of the proposed method. |
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Keywords: | Inverse problem Heat source Variational method Conjugate gradient method |
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