Seminar 18.3.2019: Marcel Braukhoff

Seminar on Qualitative Theory of Differential Equations
organized by P.Quittner, M.Fila and R.Kollar

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Seminar 18.3.2019: Marcel Braukhoff

Postby quittner » Thu Mar 07, 2019 2:32 pm

Seminár z kvalitatívnej teórie diferenciálnych rovníc
Seminar on Qualitative Theory of Differential Equations

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

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.
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