REGULARITY ANALYSIS FOR SYSTEMS OF REACTION-DIFFUSION EQUATIONS - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Preprints, Working Papers, ... Year : 2009

REGULARITY ANALYSIS FOR SYSTEMS OF REACTION-DIFFUSION EQUATIONS

Abstract

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
Fichier principal
Vignette du fichier
GoVa_revised.pdf (286.91 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

inria-00384366 , version 1 (16-05-2009)

Identifiers

  • HAL Id : inria-00384366 , version 1

Cite

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

Share

Gmail Facebook X LinkedIn More