A unified approach to solving some inverse problems for evolution equations by using observability inequalities

Kaïs Ammari (1, 2) , Mourad Choulli (3) , Faouzi Triki (4)

1 Département de Mathématiques [Monastir]
2 LMV - Laboratoire de Mathématiques de Versailles
3 IECL - Institut Élie Cartan de Lorraine
4 EDP - Equations aux Dérivées Partielles

We survey some of our recent results on inverse problems for evolution equations. The goal is to provide an unified approach to solve various type 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.

Domaines: Equations aux dérivées partielles [math.AP]

Kaïs Ammari, Mourad Choulli, Faouzi Triki. A unified approach to solving some inverse problems for evolution equations by using observability inequalities. CSIAM Transactions on Applied Mathematics, 2020, 1 (2), pp.207-239. ⟨10.4208/csiam-am.2020-0001⟩. ⟨hal-01628732v2⟩