A Unified Approach to Solving Some Inverse Problems for Evolution Equations by Using Observability Inequalities
Year: 2020
Author: Kaïs Ammari, Mourad Choulli, Faouzi Triki
CSIAM Transactions on Applied Mathematics, Vol. 1 (2020), Iss. 2 : pp. 207–239
Abstract
We survey some of our recent results on inverse problems for evolution equations. The goal is to provide a unified approach to solve various types of evolution equations. The inverse problems we consider consist in determining unknown coefficients from boundary measurements by varying initial conditions. Based on observability inequalities and a special choice of initial conditions, we provide uniqueness and stability estimates for the recovery of volume and boundary lower order coefficients in wave and heat equations. Some of the results presented here are slightly improved from their original versions.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/csiam-am.2020-0001
CSIAM Transactions on Applied Mathematics, Vol. 1 (2020), Iss. 2 : pp. 207–239
Published online: 2020-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 33
Keywords: Evolution equations Laplace-Beltrami operator observability inequality geometric control initial-to-boundary operator.
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