Multizonal boundary and internal layers in the singularly perturbed problems for a stationary equation of reaction–advection–diffusion type with weak and discontinuous nonlinearity

A singularly perturbed Dirichlet boundary value problem for a stationary equation of reaction–advection–diffusion type with multiple roots of the degenerate equation is studied. This is a new class of problems with discontinuous reactive and weak advective terms. The existence of a contrast structure solution is proved by using the method of asymptotic differential inequalities and matching asymptotic expansion. And we show that the multiple roots lead to the formation of multizonal boundary and internal layers in the neighborhood of the boundary and the discontinuity point, which is essentially quite different from the case of isolated roots.