Formation of stationary interfaces in the fast reaction limit

Abstract: We study a two-component reaction-diffusion system in which one of the reaction terms becomes singularly large. Assuming that the initial data are nonnegative and mutually segregated, we prove that the solution converges to that of the heat equation in the nonreactive region, while it remains zero elsewhere. The analysis is based on explicitly constructed barrier functions and a comparison argument adapted to systems with asymmetric reaction terms, which together provide control near the interface. As a result, the limiting behavior exhibits a stationary phase interface determined by the initial support of the reactive component.