On a two-dimensional reaction-diffusion system with hypercyclical structure

A one-dimensional reaction/diffusion system with a fast reaction

We consider a system of second order ordinary differential equations describing steady state for a 3–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 the rate of the fast reaction approaches infinity.

Chapter 7 Two-Dimensional Reaction-Diffusion Brusselator System

A two-scale reaction-diffusion system with micro-cell reaction concentrated on a free boundary

We discuss the fast-reaction limit of a two-scale reaction-diffusion model. We point out that if the reaction constant a explodes to infinity, then a two-scale PDEs system with free boundary at the micro cell is obtained. The aim of this note is to answer the question: Can the same two-scale free-boundary problem be obtained if we first pass to the fast-reaction limit a → ∞ and then take the ho...

Fast-reaction asymptotics for a two-scale reaction-diffusion system

We investigate a reaction–diffusion process in a two-phase medium with microscopic length scale ε. The diffusion coefficients in the two phases are highly different (d1/D = ε2) and the reaction constant k is large. First, the homogenisation limit ε → 0 is taken, which leads to a two-scale model. Afterwards, we pass to the fast-reaction limit k →∞ and obtain a two-scale reaction-diffusion system...

The two-dimensional reaction-diffusion Brusselator system: a dual-reciprocity boundary element solution

The dual-reciprocity boundary element method is applied for the numerical solution of a class of two-dimensional initial-boundary value problems governed by a non-linear system of partial differential equations. The system, known as the reaction-diffusion Brusselator, arises in the modeling of certain chemical reaction-diffusion processes. Numerical results are presented for some specific probl...