SEMINARS
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Fall 2005
STATISTICS
COLLOQUIUM
Friday, September 30, 2005
2:30-3:00—Refreshments
3:00-4:00—Talk
Yost Hall, Room 300
Piotr Biler
University of Wroclaw, POLAND
On a Non-Linear Diffusion Equation Related to Chemotaxis
The chemotaxis is a phenomenon of movement of microorganisms (amoebea, bacteriae) towards the higher concentration of a chemical (chemoattractant) secreted by themselves. This can be modeled either by a stochastic differential equation or by a system of parabolic-elliptic equations whose solutions, e.g., may cease to exist in finite time (which describes the aggregation of those organisms). In the radially symmetric case, the model can be simplified to a single nonlinear parabolic equation with a singular diffusion term. We study long time behavior of its solutions. The asymptotics appears to be rather complicated and sensitive to modifications of boundary conditions.
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