Orateur
Description
In its first part, this presentation revisits a basic question from parabolic regularity theory, and discusses some recent developments concerned with heat semigroup estimates and Gagliardo-Nirenberg interpolation involving certain Orlicz type expressions.
An outcome of this is thereafter applied to a taxis-type parabolic model for the dynamics of microbial populations in nutrient-poor environments, containing some cross-degenerate diffusion mechanism as a core characteristic.
The intention here is to outline an approach which, by relying on a result achieved in the first part in a crucial place, facilitates an appropriate control of such cross-degeneracies. In convex planar domains, this leads not only to a fairly comprehensive theory of global solvability, but also to a description of large time behavior and structure formation.