Planar Traveling Waves For Nonlocal Dispersion Equation With Monostable Nonlinearity

In this paper, we study a class of nonlocal dispersion equation with monostable nonlinearity in n-dimensional space uₜ - J u +u+d (u (t, x) ) = ₑ䂞 f_β (y) b (u (t-τ, x-y) ) dy, u (s, x) =u₀ (s, x), s-τ, 0, \ x Rⁿ} \] where the nonlinear functions d (u) and b (u) possess the monostable characters like Fisher-KPP type, f_β (x) is the heat kernel, and the kernel J (x) satisfies J (ξ) =1-K|ξ|^α+o (|ξ|^α) for 00, and the critical wavefronts ϕ (x e+c_*t) are globally stable in the algebraic form t^-n/α. The adopted approach is Fourier transform and the weighted energy method with a suitably selected weight function. These rates are optimal and the stability results significantly develop the existing studies for nonlocal dispersion equations.