Periodic Solutions to the Dirichlet Boundary Value Problem for a Quasilinear Parabolic Equation with Low Diffusivity

摘要

Consider the singularly perturbed boundary value problem Lε[u]=-ut+εuxx-A(u,x,t)ux-B(u, x, t) = 0, (x,t)∈ Ω = {(x,t):a 0 is a small parameter. It is assumed that(I) A, B ∈ C2(R x Ω-tilde) and ua, ub ∈ C2(R) are periodic functions of t with the same period T > 0.