REGULARITY ANALYSIS FOR SYSTEMS OF REACTION-DIFFUSION EQUATIONS

Thierry Goudon (1) , Alexis Vasseur (2)

1 SIMPAF - SImulations and Modeling for PArticles and Fluids
2 Department of Mathematics and Statistics [Texas Tech]

This paper is devoted to the study of the regularity of solutions to some systems of reaction–diffusion equations. In particular, we show the global boundedness and regularity of the solutions in one and two dimensions. In addition, we discuss the Hausdorff dimension of the set of singularities in higher dimensions. Our approach is inspired by De Giorgi's method for elliptic regularity with rough coefficients. The proof uses the specific structure of the system to be considered and is not a mere adaptation of scalar techniques; in particular the natural entropy of the system plays a crucial role in the analysis

Domaines: Equations aux dérivées partielles [math.AP]

Thierry Goudon, Alexis Vasseur. REGULARITY ANALYSIS FOR SYSTEMS OF REACTION-DIFFUSION EQUATIONS. 2009. ⟨inria-00384366⟩