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 phi(xi) with critical minimal speed c = c* decays exponentially as oo, while other traveling wave solutions phi(xi) with c > c* do not decay exponentially as xi -> -infinity. 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. (C) 2012 Elsevier Inc. All rights reserved.