Global regularity of solutions to systems of reaction-diffusion with<br/><br/>sub-quadratic growth in any dimension

Thursday, July 30, 2009 - 11:00am - 11:50am
EE/CS 3-180
Alexis Vasseur (The University of Texas at Austin)
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.
MSC Code: