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

Pages: 49 - 59, Volume 5, Issue 1, February 2012

doi:10.3934/dcdss.2012.5.49       Abstract        References        Full Text (355.5K)       Related Articles

Dieter Bothe - Center of Smart Interfaces, Technical University Darmstadt, Petersenstr. 32, 64287 Darmstadt, Germany (email)
Michel Pierre - ENS Cachan Bretagne, IRMAR, EUB, Campus de Ker Lann, 35170 Bruz, France (email)

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.

Keywords:  Chemical reaction interface, instantaneous chemical reaction, spatial segregation, Stefan-type problem.
Mathematics Subject Classification:  Primary: 35K57; Secondary: 35B25, 92E20.

Received: August 2009;      Revised: January 2010;      Published: February 2011.

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