Periodic solutions to the Dirichlet boundary value problem for a quasilinear parabolic equation with low diffusivity (Q2455325)

This paper concerns time-periodic scalar reaction-diffusion-advection equations of the type \(-u_t+\varepsilon u_{xx}-A(u,x,t)u_x-B(u,x,t)=0\), \(a<x<b\), with Dirichlet boundary conditions. Under suitable conditions, the existence of time-periodic solutions with boundary layers and/or internal layers is proved. Moreover, the periodic transformation of boundary layers into step like contrast structures and/or into interior transition layers is described.