A Unified Approach to Solving Some Inverse Problems for Evolution Equations by Using Observability Inequalities

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.

Author Details

Kaïs Ammari

Mourad Choulli

Faouzi Triki

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