| Summary: | In this article we consider a nonlinear large reaction small diffusion problem which has two (or more) stable states, and we analyse it using two different methods. First method: an approach based on (asymptotic) expansions; and second method: an approach based on the notion of $\Gamma$-convergence. The analysis of such a problem shows that the two methods are complementary. It is well known that, for such a problem, time-dependent solutions are characterised by (moving) layers or vortices. Here, we are specially interested in the existence, the shape and the motion of such layers or vortices, with respect to the inhomogeneous coefficients appearing in the problem as well as the domain $\Omega$. We generalise, in the limit of small diffusion, the usual motion by mean curvature laws found for homogeneous problems.
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