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

For a singularly perturbed reaction–diffusion equation, we study the structure of theinternal transition layer in the case of a balanced reaction with a weak discontinuity. Theexistence of solutions with an internal transition layer (contrast structures) is proved, the questionof their stability is investigated, and asymptotic approximations to solutions of this type areobtained. 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 offinite size, both stable and unstable.