Regularity analysis for systems of reaction-diffusion equations

Thierry Goudon; Alexis Vasseur

Annales scientifiques de l'École Normale Supérieure (2010)

  • Volume: 43, Issue: 1, page 117-142
  • ISSN: 0012-9593

Abstract

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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.

How to cite

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Goudon, Thierry, and Vasseur, Alexis. "Regularity analysis for systems of reaction-diffusion equations." Annales scientifiques de l'École Normale Supérieure 43.1 (2010): 117-142. <http://eudml.org/doc/272185>.

@article{Goudon2010,
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.},
author = {Goudon, Thierry, Vasseur, Alexis},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {reaction-diffusion systems; regularity of solutions},
language = {eng},
number = {1},
pages = {117-142},
publisher = {Société mathématique de France},
title = {Regularity analysis for systems of reaction-diffusion equations},
url = {http://eudml.org/doc/272185},
volume = {43},
year = {2010},
}

TY - JOUR
AU - Goudon, Thierry
AU - Vasseur, Alexis
TI - Regularity analysis for systems of reaction-diffusion equations
JO - Annales scientifiques de l'École Normale Supérieure
PY - 2010
PB - Société mathématique de France
VL - 43
IS - 1
SP - 117
EP - 142
AB - 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.
LA - eng
KW - reaction-diffusion systems; regularity of solutions
UR - http://eudml.org/doc/272185
ER -

References

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