Well-posedness of an integro-differential model for active Brownian particles

par Simon Michael Schulz (University of Wisconsin-Madison)

mardi 11 juil. 2023, 15:15 → 16:15 Europe/Paris

Fokko du Cloux (Bâtiment Braconnier, La Doua)

The focus of this talk will be to present recent results concerning macroscopic models for active Brownian particles with repulsive interactions; consisting of advection-diffusion processes both in particle position and orientation. In particular, we establish the existence and uniqueness for a model described by a semilinear parabolic equation with a nonlinear active drift term. This nonlinear term is nonlocal, as it depends on an angle-independent overall particle density; the structure of the PDE is similar to some variants of the Vlasov equation in kinetic theory. We will also briefly touch upon current works in progress related to degenerate models and quantitative regularity methods.