ИСТИНА

We consider a boundary value problem for a singularly perturbed system of fast and slow reaction-diffusion-advection equations. Using Vasilieva’s method, we construct asymptotic expansions in the small parameter for boundary layer solutions under the specified boundary conditions. An essential feature of this problem is that the stretched variables used to determine boundary layer functions at the left and right endpoints depend on different powers of the small parameter. Using Nefedov’s asymptotic method of differential inequalities [3], we prove existence and Lyapunov asymptotic stability theorems for solutions with the constructed asymptotics, both for quasimonotone sources and for sources without the quasimonotonicity requirement.