Department of

January 2014 February 2014 March 2014 Su Mo Tu We Th Fr Sa Su Mo Tu We Th Fr Sa Su Mo Tu We Th Fr Sa 1 2 3 4 1 1 5 6 7 8 9 10 11 2 3 4 5 6 7 8 2 3 4 5 6 7 8 12 13 14 15 16 17 18 9 10 11 12 13 14 15 9 10 11 12 13 14 15 19 20 21 22 23 24 25 16 17 18 19 20 21 22 16 17 18 19 20 21 22 26 27 28 29 30 31 23 24 25 26 27 28 23 24 25 26 27 28 29 30 31

Tuesday, February 4, 2014

**Abstract:** 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.