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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
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https://hal.inria.fr/inria-00384366
Contributor : Thierry Goudon <>
Submitted on : Saturday, May 16, 2009 - 12:38:28 AM
Last modification on : Friday, November 27, 2020 - 2:18:02 PM
Long-term archiving on: : Thursday, June 10, 2010 - 11:12:20 PM

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  • HAL Id : inria-00384366, version 1

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

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