Nonlinear Reaction-Diffusion Problems with Multivalued Interface Conditions: analysis and numerical perspectives

par Marion Meutelet (IDP Tours)

jeudi 9 avr. 2026, 14:00 → 15:00 Europe/Paris

E2290 (Tours)

We study nonlinear reaction-diffusion problems in compartmentalized domains, coupled through multivalued interface laws. Such models arise in biological applications, where transmission across membranes or narrow channels can involve threshold effects or congestion.
The coupling is described by a graph relating traces and fluxes at the interface. Using a framework based on broken Sobolev spaces, we analyze the associated stationary problem and prove existence and uniqueness of weak solutions under an accretivity assumption.
This approach is connected to accretive operator theory and the Crandall-
Liggett theorem for evolution problems. We also introduce a fnite volume
scheme adapted to the interface structure, and discuss perspectives towards
multiscale models inspired by organ-on-chip applications.