Periodic Inner Transition Layers in the Reaction–Diffusion Problem in the Case of Weak Reaction Discontinuity

Abstract

For a singularly perturbed reaction–diffusion equation with periodic coefficients, the structure of the inner transition layer in the case of a balanced reaction with a weak discontinuity is investigated. The existence of periodic solutions with an inner transition layers is proven, their stability is analyzed, and asymptotic approximations of solutions of this type are obtained. It is demonstrated that in the case of reaction balance, the presence of even a weak (asymptotically small) reaction discontinuity can lead to the formation of several periodic contrast structures of finite size, both stable and unstable.