Asymptotic behavior of traveling fronts and entire solutions for a nonlocal monostable equation

This paper is concerned with the asymptotic behavior of traveling fronts and entire solutions for a nonlocal monostable equation. The asymptotic behavior of traveling fronts is obtained using Ikehara’s Theorem. By the sub–super-solution method, the existence of entire solutions is obtained; they behave as two opposite wave fronts approaching each other from either side of the x -axis and then annihilating in a finite time. By an entire solution we mean one which is defined over the whole space for all time t ∈ R .