The instantaneous limit for reaction-diffusion systems with a fast irreversible reaction

Dieter Bothe; Michel Pierre

doi:10.3934/dcdss.2012.5.49

Article Contents

2012, Volume 5, Issue 1: 49-59. Doi: 10.3934/dcdss.2012.5.49

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The instantaneous limit for reaction-diffusion systems with a fast irreversible reaction

Dieter Bothe^1, and
Michel Pierre^2,

1.
Center of Smart Interfaces, Technical University Darmstadt, Petersenstr. 32, 64287 Darmstadt
2.
ENS Cachan Bretagne, IRMAR, EUB, Campus de Ker Lann, 35170 Bruz

Received: July 31, 2009

Revised: December 31, 2009

Published: January 2012

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Abstract

We consider reaction-diffusion systems which, in addition to certain slow reactions, contain a fast irreversible reaction in which chemical components A and B form a product P. In this situation and under natural assumptions on the RD-system we prove the convergence of weak solutions, as the reaction speed of the irreversible reaction tends to infinity, to a weak solution of a limiting system. The limiting system is a Stefan-type problem with a moving interface at which the chemical reaction front is localized.

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Mathematics Subject Classification: Primary: 35K57; Secondary: 35B25, 92E20.

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