Kinetic Description of Multiscale Phenomena

The Annual Kinetic FRG Meeting
September 21-25, 2009

CSIC Building (#406), Seminar Room 4122.

Global regularity for a class of systems of reaction-diffusion equations

Dr. Alexis Vasseur

University of Texas at Austin

Abstract:  In this talk, we present the study of the regularity of solutions to some systems of reaction-diffusion equations, with reaction terms having a subquadratic growth. We show the global boundedness and regularity of solutions, without smallness assumptions, in any dimension N. The proof is based on blow-up techniques. The natural entropy of the system plays a crucial role in the analysis. It allows us to use of De Giorgi type methods introduced for elliptic regularity with rough coefficients. Even if those systems are entropy supercritical, it is possible to control the hypothetical blow-ups, in the critical scaling, via a very weak norm.