26453 articles – 20338 references  [version française]
Short view Article in peer-reviewed journal
Global existence for quadratic systems of reaction-diffusion
Desvillettes L. et al
advanced nonlinear studies 7, 3 (2007) 491-511 - http://hal.archives-ouvertes.fr/hal-00364787
Laurent Desvillettes ()1, Klemens Fellner ()2, Michel Pierre ()3, Julien Vovelle ()3, 4
1:  CMLA - Centre de Mathématiques et de Leurs Applications
http://www.cmla.ens-cachan.fr/Cmla/index.html
CNRS : UMR8536 – École normale supérieure (ENS) - Cachan
France
2:  Fakultät für Mathematik
http://homepage.univie.ac.at/
Universität Wien
Nordbergstrasse 15, 1090 Wien, Austria
Austria
3:  IRMAR - Institut de Recherche Mathématique de Rennes
http://irmar.univ-rennes1.fr/
CNRS : UMR6625 – Université de Rennes 1 – École normale supérieure (ENS) - Cachan – Institut National des Sciences Appliquées [INSA] : - RENNES – Université de Rennes II - Haute Bretagne
France
4:  LATP - Laboratoire d'Analyse, Topologie, Probabilités
http://www.latp.univ-mrs.fr
CNRS : UMR6632 – Université de Provence - Aix-Marseille I – Université Paul Cézanne - Aix-Marseille III
39 rue Joliot-Curie 13453 Marseille Cedex 13
France
Mathematics/Numerical Analysis
Global existence for quadratic systems of reaction-diffusion
We prove global existence in time of weak solutions to a class of quadratic reaction-diffusion systems for which a Lyapounov structure of LlogL-entropy type holds. The approach relies on an a priori dimension-independent L-2-estimate, valid for a wider class of systems includingalso some classical Lotka-Volterra systems, and which provides an L-1-bound on the nonlinearities, at least for not too degenerate diffusions. In the more degenerate case, some global existence may be stated with the use of a weaker notion of renormalized solution with defect measure, arising in the theory of kinetic equations.
English

advanced nonlinear studies
international
2007
7
3
491-511

reaction-diffusion system – Lotka-Volterra systems – weak solutions – renormalized solutions – global existence – entropy methods
35K57