Title: Nonnegative solutions to a doubly degenerate nutrient taxis system in planar domains
Speaker: Michael Winkler
Time: Saturday, March 14, 2026, 16:00-17:00
Zoom ID: 921 4145 5393
Password: 260314
Abstract: A taxis-type parabolic model for the dynamics of microbial populations in nutrient-poor environments is considered, containing a doubly degenerate diffusion mechanism as a core characteristic. Systems of this form have been proposed to describe complex pattern formation experimentally observed in colonies of Bacillus subtilis when exposed to nutrient-poor environments, inter alia going along with the emergence of complex structures especially near interfaces between settled and unsettled regions. In line with mathematical challenges associated with this, previous related analytical literature has mainly concentrated on frameworks involving simplifications such as reductions to one-dimensional settings or positive initial data, or the inclusion of regularizing effects. The presentation intends to outline a recent approach, developed in collaboration with Duan Wu, which in bounded convex two-dimensional domains and for widely arbitrary nonnegative initial data is capable not only of establishing a comprehensive theory of global solvability, but also of describing large time behavior and structure formation.
