Inverse problem of reconstruction of degenerate diffusion coefficient in a parabolic equation
We consider the inverse problem of identification of degenerate diffusion coefficient of the form xαa(x) in a one dimensional parabolic equation by some extra data. We first prove by energy methods the uniqueness and Lipschitz stability results for the identification of a constant coefficient a and...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2021 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/165523 |
| Acceso en línea: | https://hdl.handle.net/11441/165523 https://doi.org/10.1088/1361-6420/ac274b |
| Access Level: | acceso abierto |
| Palabra clave: | Inverse problems Degenerate parabolic equations Numerical reconstruction |
| Sumario: | We consider the inverse problem of identification of degenerate diffusion coefficient of the form xαa(x) in a one dimensional parabolic equation by some extra data. We first prove by energy methods the uniqueness and Lipschitz stability results for the identification of a constant coefficient a and the power α by knowing interior data at some time. On the other hand, we obtain the uniqueness result for the identification of a general diffusion coefficients a(x) and also the power α form boundary data on one side of the space interval. The proof is based on global Carleman estimates for a hyperbolic problem and an inversion of the integral transform similar to the Laplace transform. Finally, the theoretical results are satisfactory verified by numerically experiments. |
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