SPATIAL DYNAMICS OF THE ADVECTIVE REACTION-DIFFUSION EQUATION ON FUNNEL-SHAPED DOMAINS

This paper is concerned with the entire solution of the advective reaction-diffusion equation with the bistable nonlinear reaction term on funnel-shaped domains. We focus on the well-posedness and long-time behavior of the entire solution. Because of the impact of advection, the previous super and sub-solutions are no longer applicable, so we study the existence of the entire solution behaving as a planar front by constructing appropriate super-solutions and sub-solutions. In addition, we show the uniqueness and Lyapunov stability of the entire solution. This is probably the first study of the advective reaction-diffusion on funnel-shaped domains.