Dynamics of Partial Differential Equations

Volume 8 (2011)

Number 2

Global existence for coupled reaction diffusion systems modelling some reversible chemical reactions

Pages: 79 – 88

DOI: https://dx.doi.org/10.4310/DPDE.2011.v8.n2.a1


Said Kouachi (Department of Mathematics, Qassim University, Buraydah, Saudi Arabia)


The purpose of this paper is to prove global existence of solutions for coupled reaction diffusion equations describing some coupled reversible chemical reactions. In this case the nonlinearities present a difficulties since they change sign and so neither u nor v the concentrations of the two reactants in question is a priori bounded or at least bounded in some Lp-space for p large. Our techniques are based on Lyapunov functional method.


reaction-diffusion systems, Global existence, Lyapunov functionals

2010 Mathematics Subject Classification

35K45, 35K57

Published 23 June 2011