All Issues

Vol.14, 2024
Vol.10, 2020
Vol.9, 2019
Vol.8, 2018
Vol.7, 2017
Vol.6, 2016
Vol.5, 2015
Vol.4, 2014
Vol.3, 2013
Vol.2, 2012
Vol.1, 2011
Volume 3, Number 4, 2013, Pages 357-376                                                                DOI:10.11948/2013027
Global existence and uniqueness for a system of semilinear multi-species diffusion-reaction equations
Hari Shankar Mahato,Michael Bohm
Keywords:Global solution, semilinear parabolic equation, reversible reactions, Lyapunov functionals, maximal regularity
      In this paper, we consider a system of highly nonlinear multispecies diffusion-reaction equations with homogeneous Neumann boundary condition. All reactions are reversible (see (1.1)). For this system, the existence and uniqueness of the weak solution are proved on the interval [0; T) for any T > 0. We obtain, global in time, L∞-estimates of the solution with the help of a Lyapunov functional. For the existence of the solution, we use Schaefer’s fixed point theorem, maximal regularity and Lyapunov type arguments.
PDF      Download reader