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| An Inverse Problem of Identifying the RadiativeCoefficient in a Degenerate Parabolic Equation? |
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Citation： |
Zuicha DENG,Liu YANG.An Inverse Problem of Identifying the RadiativeCoefficient in a Degenerate Parabolic Equation?[J].Chinese Annals of Mathematics B,2014,35(3):355~382 |
| Page view： 2896
Net amount： 2306 |
Authors： |
Zuicha DENG; Liu YANG; |
Foundation： |
National Natural Science Foundation of China (Nos. 11061018,11261029), the Youth Foundation of Lanzhou Jiaotong University (No. 2011028), the Long Yuan YoungCreative Talents Support Program (No. 252003) and the Joint Funds of the Gansu Provincial NaturalScience Foundation of China (No. 1212RJZA043). |
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| Abstract： |
The authors investigate an inverse problem of determining the radiative coefficient
in a degenerate parabolic equation from the final overspecified data. Being different
from other inverse coefficient problems in which the principle coefficients are assumed to
be strictly positive definite, the mathematical model discussed in this paper belongs to
the second order parabolic equations with non-negative characteristic form, namely, there
exists a degeneracy on the lateral boundaries of the domain. Based on the optimal control
framework, the problem is transformed into an optimization problem and the existence of
the minimizer is established. After the necessary conditions which must be satisfied by the
minimizer are deduced, the uniqueness and stability of the minimizer are proved. By minor
modification of the cost functional and some a priori regularity conditions imposed on the
forward operator, the convergence of the minimizer for the noisy input data is obtained in
this paper. The results can be extended to more general degenerate parabolic equations. |
Keywords： |
Inverse problem, Degenerate parabolic equation, Optimal control, Existence,Uniqueness, Stability, Convergence |
Classification： |
35R30, 49J20 |
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