Identifying Initial Condition in Degenerate Parabolic Equation with Singular Potential
A hybrid algorithm and regularization method are proposed, for the first time, to solve the one-dimensional degenerate inverse heat conduction problem to estimate the initial temperature distribution from point measurements. The evolution of the heat is given by a degenerate parabolic equation with...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2017-01-01
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| Series: | International Journal of Differential Equations |
| Online Access: | http://dx.doi.org/10.1155/2017/1467049 |
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| Summary: | A hybrid algorithm and regularization method are proposed, for the first time, to solve the one-dimensional degenerate inverse heat conduction problem to estimate the initial temperature distribution from point measurements. The evolution of the heat is given by a degenerate parabolic equation with singular potential. This problem can be formulated in a least-squares framework, an iterative procedure which minimizes the difference between the given measurements and the value at sensor locations of a reconstructed field. The mathematical model leads to a nonconvex minimization problem. To solve it, we prove the existence of at least one solution of problem and we propose two approaches: the first is based on a Tikhonov regularization, while the second approach is based on a hybrid genetic algorithm (married genetic with descent method type gradient). Some numerical experiments are given. |
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| ISSN: | 1687-9643 1687-9651 |