### Laboratoire d'accueil

CNRS Orleans /University of Orleans - FR

Mathematics - Analysis, Probability, Modelling (MAPMO)

### Hôte scientifique

Pr Jérôme Le Rousseau

## PROJET

**On control and inverse problems for partial differential equations**

Control theory and inverse problems for partial differential equations (PDEs) are at the interplay of many mathematical disciplines. Parts of those research disciplines are covered by the expertise areas of the researchers of Fédération Denis Poisson (FDP) located in both Orleans and Tours in region Centre. In particular, control theory for PDEs is an active field within FDP. Theoretical inverse problems are also addressed but less intensively.

The project focuses on particular aspects of controllability and inverse-problem questions. Relaxing assumptions on the PDE coefficients in existing results to treat models that are closer to real-word applications (variables coefficients, non-smooth coefficients). Study the case of systems of coupled PDEs (as opposed to scalar equations). Such systems occur in many models from physics and biology. Analysis tools for the treatment of control and inverse-problem questions for systems of PDEs need yet to be developed.

The work pursues fundamental questions in both inverse problems and control theory. These two fields of research are quite close to one another and advances in one field can benefit to the other one.