Boundary-Value Problem for Singularly Perturbed Integro-Differential Equation with Singularly Perturbed Neumann Boundary Condition

We consider a boundary-value problem for singularly perturbed integro-differential equation describing stationary reaction-diffusion processes with due account of nonlocal interactions. The principal feature of the problem is the presence of a singularly perturbed Neumann condition describing intense flows on the boundary. We prove that there exists a boundary-layer solution, construct its asymptotic approximation, and establish its asymptotic Lyapunov stability. Illustrative examples are given.