Coefficient identification in parabolic equations with final data
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.
Cite
@article{arxiv.2005.05193,
title = {Coefficient identification in parabolic equations with final data},
author = {Faouzi Triki},
journal= {arXiv preprint arXiv:2005.05193},
year = {2020}
}