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An existence result for a system of coupled semilinear diffusion-reaction equations with flux boundary conditions

Published online by Cambridge University Press:  10 December 2014

HARI SHANKAR MAHATO  and
MICHAEL BÖHM
HARI SHANKAR MAHATO
Affiliation:
Chair of Applied Mathematics 1, University of Erlangen-Nürnberg, 91058 Erlangen, Germany email: mahato@math.fau.de
MICHAEL BÖHM
Affiliation:
Center of Industrial Mathematics, University of Bremen, 28359 Bremen, Germany
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Abstract

In this paper, we consider diffusion, reaction and dissolution of mobile and immobile chemical species present in a porous medium. Inflow–outflow boundary conditions are considered at the outer boundary and the reactions amongst the species are assumed to be reversible which yield highly nonlinear reaction rate terms. The dissolution of immobile species takes place on the surfaces of the solid parts. Modelling of these processes leads to a system of coupled semilinear partial differential equations together with a system of ordinary differential equations (ODEs) with multi-valued right-hand sides. We prove the global existence of a unique positive weak solution of this model using a regularization technique, Schaefer's fixed point theorem and Lyapunov type arguments.

Keywords

Global solutionsemilinear parabolic equationreversible reactionsLyapunov functionalsmaximal regularity
Type
Papers
Information
European Journal of Applied Mathematics , Volume 26 , Issue 2 , April 2015 , pp. 121 - 142
Copyright
Copyright © Cambridge University Press 2014 

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