Solution of contrast structure type for a reaction-diffusion equation with discontinuous reactive term

Abstract

In this paper, we consider the Dirichlet boundary value problem for a singularly perturbed reaction-diffusion equation with discontinuous reactive term. We use the asymptotic analysis to construct the formal asymptotic approximation of the solution with internal and boundary layers. The internal layer is located in the vicinity of a curve of the discontinuous reactive term. By using sufficiently precise lower and upper solutions, we prove the existence of a periodic solution and estimate the accuracy of its asymptotic approximation.

Geometric singular perturbation of a nonlocal partially degenerate model for <i>Aedes aegypti</i>

“…Moreover, Du and his collaborators [8,9,10] discussed the existence of TWS for a series of models by utilizing the GSP theory. It should be pointed out that the theory of GSP can be used not only to study the existence of TWS, but also to deal with other problems [6,18,24,38].…”