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- W4287779306 abstract "In this work we determine the second-order coefficient in a parabolic equation from the knowledge of a single final data. Under assumptions on the concentration of eigenvalues of the associated elliptic operator, and the initial state, we show the uniqueness of solution, and we derive a Lipschitz stability estimate for the inversion when the final time is large enough. The Lipschitz stability constant grows exponentially with respect to the final time, which makes the inversion ill-posed. The proof of the stability estimate is based on a spectral decomposition of the solution to the parabolic equation in terms of the eigenfunctions of the associated elliptic operator, and an ad hoc method to solve a nonlinear stationary transport equation that is itself of interest." @default.
- W4287779306 created "2022-07-26" @default.
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- W4287779306 date "2020-05-11" @default.
- W4287779306 modified "2023-09-23" @default.
- W4287779306 title "Coefficient identification in parabolic equations with final data" @default.
- W4287779306 doi "https://doi.org/10.48550/arxiv.2005.05193" @default.
- W4287779306 hasPublicationYear "2020" @default.
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