Existence and stability of periodic curved traveling fronts for nonlocal dispersal equations with periodic bistable nonlinearity

In this paper, we study the curved traveling fronts of nonlocal dispersal equations with time-periodic bistable nonlinearity in two dimensional space. By constructing appropriate super-solutions and sub-solutions, and using the fixed point theory and functional analysis skills, we first establish the existence result of the periodic curved traveling fronts. Then, we prove that the periodic curved traveling fronts are asymptotically stable. Although the results are similar to the corresponding classical equations with time-periodic bistable nonlinearity, the proofs are quite different.