Internal Transition Layer Structure in the Reaction–Diffusion Problem for the Case of a Balanced Reaction with a Weak Discontinuity

Abstract

For a singularly perturbed reaction–diffusion equation, we study the structure of the internal transition layer in the case of a balanced reaction with a weak discontinuity. The existence of solutions with an internal transition layer (contrast structures) is proved, the question of their stability is investigated, and asymptotic approximations to 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 discontinuity can lead to the formation of contrast structures of finite size, both stable and unstable.