Reaction-diffusion fronts in funnel-shaped domains

We consider bistable reaction-diffusion equations in funnel-shaped domains of RN made up straight parts and conical with positive opening angles. study the large time dynamics entire solutions emanating from a planar front part such domain moving into part. show dichotomy between blocking spreading, by proving especially some new Liouville type results on stable semilinear elliptic whole space RN. also that any spreading solution is transition having global mean speed, which unique speed fronts, it converges at to well-formed whose position approximated expanding spheres. Moreover, we provide sufficient conditions size R angle α part, under blocked or spreads completely finally openness set parameters (R,α) for propagation complete.