Existence and stability of periodic contrast structure in reaction-advection-diffusion equation with discontinuous reactive and convective terms

In this project, we study the periodic Dirichlet boundary value problem for a singularly perturbed reaction-advection-diffusion equation on the segment in case of discontinuous reactive and convective terms. Applying the boundary function method, we construct the asymptotic approximation of the periodic solution with internal transition layer located in the vicinity of a curve of discontinuity of the mentioned terms. For the problem here we prove the existence of the periodic solution, estimate the accuracy of the asymptotical approximation and investigate the stability of the periodic solution as solutions of the corresponding initial boundary value problems for the reaction-advection-diffusion equation.