Spreading speeds and traveling waves for nonlocal dispersal equations with degenerate monostable nonlinearity

This paper is concerned with the spreading speeds and traveling wave solutions of a nonlocal dispersal equation with degenerate monostable nonlinearity. We first prove that the traveling wave solution ϕ(ξ) with critical minimal speed c=c⁎ decays exponentially as ξ→−∞, while other traveling wave solutions ϕ(ξ) with c>c⁎ do not decay exponentially as ξ→−∞. Then the monotonicity and uniqueness (up to translation) of traveling wave solution with critical minimal speed is established. Finally, we prove that the critical minimal wave speed c⁎ coincides with the asymptotic speed of spread.