Young Researchers Workshop:
Kinetic and macroscopic models for complex systems

Enhancement of biological reaction by chemotaxis

Yao Yao

University of Wisconsin-Madison

In this talk, we consider a system of equations arising from reproduction processes in biology, where two densities evolve under diffusion, absorbing reaction and chemotaxis. We prove that chemotaxis plays a crucial role to ensure the efficiency of reaction: Namely, the reaction between the two densities is very slow in the pure diffusion case, while adding a chemotaxis term greatly enhances reaction. While proving our main results we also obtain a weighted Poincare's inequality for the Fokker-Planck equation, which might be of independent interest.

This is a joint work with A. Kiselev, F. Nazarov and L. Ryzhik.