The exact boundary behavior of the unique solution to a singular Dirichlet problem with a nonlinear convection term

Abstract

In this paper we analyze the exact boundary behavior of the unique solution to the singular nonlinear Dirichlet problem −△u=b(x)g(u)+λ|∇u|q,u>0,x∈Ω,u|∂Ω=0, where Ω is a bounded domain with smooth boundary in RN, q∈(0,2], λ≥0, g∈C1((0,∞),(0,∞)), lims→0+g(s)=∞, g is decreasing on (0,∞), and b∈Clocα(Ω), is positive in Ω, may be vanishing or singular on the boundary. We reveal that the nonlinear convection term λ|∇u|q does not affect the first expansion of the unique solution near the boundary to the problem.