  In this paper, we present an approach to characterising fast-reaction limits
of systems with nonlinear diffusion, when there are either two
reaction-diffusion equations, or one reaction-diffusion equation and one
ordinary differential equation, on unbounded domains. Here, we replace the
terms of the form uxx in usual reaction-diffusion equation, which represent
linear diffusion, by terms of form phi(u)xx, representing nonlinear diffusion.
We prove the convergence as k tends to infinity to a limit that is determined
by the unique solution of a certain scalar nonlinear diffusion limit problem.
