Fast propagation for nonlocal delay equations with slowly decaying initial values. (English) Zbl 1254.35027
Summary: This article concerns the long time behavior of solutions to nonlocal delay equations when the initial values decay slowly at infinity towards the unstable steady state. By constructing proper auxiliary functions, it is proved that the lower bounds of asymptotic speed for spreading is larger any given positive constant, which implies the fast propagation.
MSC:
35B40 | Asymptotic behavior of solutions to PDEs |
35C07 | Traveling wave solutions |
35K57 | Reaction-diffusion equations |
37C65 | Monotone flows as dynamical systems |