Spreading speeds and traveling waves for fractional equations with degenerate reactions

This paper focuses on studying the propagation phenomenon for fractional equations with degenerate reactions. Specifically, we prove the existence of a minimum traveling wave speed denoted by c ∗ c^* so that traveling waves exist with any speed c ≥ c ∗ c\geq c^* and non-existence of traveling waves with speed c > c ∗ c>c^* . Furthermore, we prove that c ∗ c^* is precisely the spreading speed and provides a Volpert-Volpert-Volpert type variational characterization for it in the homogeneous case. Our method is mainly based on monotone dynamic theory.