Fast reaction limit of reaction-diffusion systems

Global existence and fast-reaction limit in reaction-diffusion systems with cross effects

A Fast Solver for Systems of Reaction-Diffusion Equations

Here, u is a vector-valued function, u ≡ u(x, t) ∈ R, m is large, and the corresponding system of ODEs, ∂tu = F (x, t, u), is stiff. Typical examples arise in air pollution studies, where a is the given wind field and the nonlinear function F models the atmospheric chemistry. The time integration of Eq. (1) is best handled by the method of characteristics [1]. The problem is thus reduced to des...

Multispecies reaction-diffusion systems

Multispecies reaction-diffusion systems, for which the time evolution equations of correlation functions become a closed set, are considered. A formal solution for the average densities is found. Some special interactions and the exact time dependence of the average densities in these cases are also studied. For the general case, the large-time behavior of the average densities has also been ob...

Pattern formation in reaction-diffusion and reaction-diffusion-convection systems

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.