Interaction of Traveling Curved Fronts in Bistable Reaction-Diffusion Equations in R2

We consider the interaction of traveling curved fronts in bistable reaction-diffusion equations in two-dimensional spaces. We first characterize the growth of the traveling curved fronts at infinity; then by constructing appropriate subsolutions and supersolutions, we prove that the solution of the Cauchy problem converges to a pair of diverging traveling curved fronts in R2 under appropriate initial conditions.