Electronic Journal of Differential Equations,
Vol. 2012 (2012), No. 140, pp. 1-10.

Title: Fast propagation for nonlocal delay equations with slowly decaying 
       initial values

Author: Fuguo Zhu (Hexi Univ., Zhangye, Gansu, China)

Abstract:
 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.

Submitted June 28, 2012. Published August 19, 2012.
Math Subject Classifications: 35C07, 35K57, 37C65.
Key Words: Fast propagation; traveling wave solutions; asymptotic spreading.