Internal Transition Layer in Reaction-Diffusion System in Bounded Domains

The paper considers a system of two reaction-diffusion equations with diffusion coefficients differing by several orders of magnitude and discontinuous reactive terms. The existence, local uniqueness and Lyapunov asymptotic stability of a solution with an internal transition layer are established. The analysis is carried out using asymptotic method of differential inequalities. The obtained conditions for the existence of a stable solution determine the limits of applicability of model problems based on such systems of equations, in particular, for studying chemical transformations in the pore spaces of geological formations.