GT Transport optimal - EDP - Machine learning
Boundary stabilization of cross-diffusion systems in moving domains
Oct. 2022
Oct. 2022
Intervenant : Virginie Ehrlacher
Institution : (Cermics) ENPC & (Matherials) INRIA
Heure : 15h15 - 16h15
Lieu : 3L15

The aim of this talk is to study the boundary stabilization of one-dimensional cross-diffusion systems in a moving domain. 

We show first exponential stabilization and then finite-time stabilization in arbitrary small time of the linearized system around uniform equilibria, provided the system

has an entropic structure with a symmetric mobility matrix. One example of such systems are the equations describing a Physical Vapor Deposition (PVD) process. 

This stabilization is achieved with respect to both the volumic fractions and the thickness of the domain. The feedback control is derived using the backstepping technique, 

adapted to the context of a time-dependent domain. In particular, the norm of the backward backstepping transform is carefully estimated with respect to time.

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