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

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 internal transition layers is proved, the question of their stability is investigated, and asymptotic approximations of solutions of this type are obtained. It is shown that in the case of reaction balance, the presence of even a weak (asymptotically small) reaction gap can lead to the formation of several contrasting structures of finite size, both stable and unstable.