Traveling curved fronts of bistable Lotka–Volterra competition–diffusion systems in R3R3

This paper is concerned with the existence and other qualitative properties of three-dimensional traveling curved fronts for bistable Lotka–Volterra competition–diffusion systems in R3R3. It is first shown that there exists a traveling front of convex polyhedral shape to such systems which is asymptotically stable. Then, by taking the limits of such solutions as lateral surfaces go to infinity, one proves the existence as well as the uniqueness of a three-dimensional traveling curved front for any given g∈C∞(S1)g∈C∞(S1) with min0≤θ≤2πg(θ)=0min0≤θ≤2πg(θ)=0.