On a Cross-Diffusion System with Independent Drifts: The Existence of Totally Mixed Solutions

par Guy Parker (Durham, UK)

mercredi 1 oct. 2025, 10:30 → 12:00 Europe/Paris

112 (Braconnier)

When modelling the evolution of multiple heterogeneous species, it is often realistic to assume that agents will only migrate away from areas of high overall population density, as opposed to dispersing away from areas which are of high density for their own species. Moreover, this principle underpins many models of tumour growth, migration and epidemiology.

 

For such models, the associated cross-diffusion systems often lack any type of self-diffusion mechanism and, consequently, solutions may produce sharp inter-species interfaces which coincide with the existence of jump discontinuities.

In this talk, I will discuss the challenges presented in establishing the well-posedness of such systems with a particular emphasis on new work, which concerns the existence of solutions in the presence of additional convective effects which may vary between each species.