Traveling wave front and stability as planar wave of reaction diffusion equations with nonlocal delays

Abstract

This paper is concerned with traveling wave front and the stability as planar wave of reaction diffusion system on $${\mathbb{R}^{n}}$$ , where n ≥ 2. Existence and asymptotic behavior of traveling wave front are discussed firstly. The stability as planar wave is established secondly by using super-sub solution method. Under initial perturbation that decays at space infinity, the perturbed solution converges to planar wave as $${t \rightarrow {\infty}}$$ and the convergence is uniform in $${\mathbb{R}^{n}}$$ .