Seminar on Qualitative Theory of Differential Equations - Marcel Braukhoff (18.3.2019)
Monday 18.3.2019 at 14:00, Lecture room M/223
Marcel Braukhoff (TU Wien):
Stationary solutions to a chemotaxis-consumption model with realistic boundary conditions
Abstract:
In the talk we discuss the behavior of the concentration of some bacteria (for example of the species Bacillus subtilis), whose otherwise random motion is partially directed towards higher concentrations of a signaling substance (oxygen) they consume. After a transition phase, the system can be described using the stationary chemotaxis model. Previous studies of chemotaxis models with consumption of the chemoattractant (with or without fluid) have not been successful in explaining pattern formation even in the simplest form of concentration near the boundary, which had been experimentally observed.
Following the suggestions that the main reason for that is usage of inappropriate boundary conditions, this talks considers physically meaningful boundary conditions for the signaling substance. We discuss the existence and uniqueness as well as properties of non-trivial solutions for given fixed mass.