Global existence for reaction–diffusion systems with nonlinear diffusion and control of mass

  • El Haj Laamri

    Institut Elie Cartan, Université de Lorraine, B.P 239, 54506 Vandœuvre-lès-Nancy, France
  • Michel Pierre

    Ecole Normale Supérieure de Rennes, IRMAR, UEB, Campus de Ker Lann, 35170 Bruz, France

Abstract

We prove here global existence in time of weak solutions for some reaction–diffusion systems with natural structure conditions on the nonlinear reactive terms which provide positivity of the solutions and uniform control of the total mass. The diffusion operators are nonlinear, in particular operators of the porous media type . Global existence is proved under the assumption that the reactive terms are bounded in . This extends previous similar results obtained in the semilinear case when the diffusion operators are linear of type .

Cite this article

El Haj Laamri, Michel Pierre, Global existence for reaction–diffusion systems with nonlinear diffusion and control of mass. Ann. Inst. H. Poincaré Anal. Non Linéaire 34 (2017), no. 3, pp. 571–591

DOI 10.1016/J.ANIHPC.2016.03.002