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A reaction–diffusion system with fast reversible reaction

✍ Scribed by D. Bothe; D. Hilhorst

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
210 KB
Volume
286
Category
Article
ISSN
0022-247X

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✦ Synopsis

We consider a reaction-diffusion system which models a fast reversible reaction between two mobile reactants and prove convergence of the solutions as the reaction rate tends to infinity, where the limiting problem is given by a diffusion equation with nonlinear diffusion. Since the rate function has no sign, the usual methods to obtain a priori estimates in the case of irreversible reactions do not apply; we deduce instead a priori estimates from computations based on Lyapunov function techniques.

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We consider a system of second-order ordinary differential equations describing Ž . steady state for a three-component chemical system with diffusion in the case when one of the reactions is fast. We discuss the existence of solutions and the existence, uniqueness, and characterization of a limit as