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Volume 1, Issue 2
A Unified Approach to Solving Some Inverse Problems for Evolution Equations by Using Observability Inequalities

Kaïs Ammari, Mourad Choulli & Faouzi Triki

DOI: 10.4208/csiam-am.2020-0001

CSIAM Trans. Appl. Math., 1 (2020), pp. 207-239.

Published online: 2020-07

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  • 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.

  • Keywords

Evolution equations, Laplace-Beltrami operator, observability inequality, geometric control, initial-to-boundary operator.

  • AMS Subject Headings

35R30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CSIAM-AM-1-207, author = {Ammari , KaïsChoulli , Mourad and Triki , Faouzi}, title = {A Unified Approach to Solving Some Inverse Problems for Evolution Equations by Using Observability Inequalities}, journal = {CSIAM Transactions on Applied Mathematics}, year = {2020}, volume = {1}, number = {2}, pages = {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.

}, issn = {2708-0579}, doi = {https://doi.org/10.4208/csiam-am.2020-0001}, url = {http://global-sci.org/intro/article_detail/csiam-am/17176.html} }
TY - JOUR T1 - A Unified Approach to Solving Some Inverse Problems for Evolution Equations by Using Observability Inequalities AU - Ammari , Kaïs AU - Choulli , Mourad AU - Triki , Faouzi JO - CSIAM Transactions on Applied Mathematics VL - 2 SP - 207 EP - 239 PY - 2020 DA - 2020/07 SN - 1 DO - http://doi.org/10.4208/csiam-am.2020-0001 UR - https://global-sci.org/intro/article_detail/csiam-am/17176.html KW - Evolution equations, Laplace-Beltrami operator, observability inequality, geometric control, initial-to-boundary operator. AB -

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.

Ammari , KaïsChoulli , Mourad and Triki , Faouzi. (2020). A Unified Approach to Solving Some Inverse Problems for Evolution Equations by Using Observability Inequalities. CSIAM Transactions on Applied Mathematics. 1 (2). 207-239. doi:10.4208/csiam-am.2020-0001
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