The instantaneous limit for reaction-diffusion systems with a fast irreversible reaction
Dieter Bothe - Center of Smart Interfaces, Technical University Darmstadt, Petersenstr. 32, 64287 Darmstadt, Germany (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.
Received: August 2009; Revised: January 2010; Published: February 2011.