Friday, April 19, 2013 - 2:00pm
1 hour (actually 50 minutes)
Univrsity of Wisconsin,-Madison
We discuss a system of two equations involving two diffusing densities, one of which is chemotactic on the other, and absorbing reaction. The problem is motivated by modeling of coral life cycle and in particular breeding process, but the set up is relevant to many other situations in biology and ecology. The models built on diffusion and advection alone seem to dramatically under predict the success rate in coral reproduction. We show that presence of chemotaxis can significantly increase reproduction rates. On mathematical level, the first step in understanding the problem involves derivation of sharp estimates on rate of convergence to bound state for Fokker-Planck equation with logarithmic potential in two dimensions.