Existence and stability of periodic solution of contrast structure type in discontinuous singularly perturbed reaction–convection–diffusion problem

A singularly perturbed periodic problem is investigated for the reaction–diffusion–advection equation in the case of a discontinuous source and weak advection. An asymptotic approximation for a periodic solution with an internal transition layer is constructed by using the boundary function method. The asymptotic method of differential inequalities is used to prove the existence of the solution and its asymptotic stability. An example is given and numerical calculations are performed to illustrate the theoretical result.