Abstract
Recently, there have been great progresses on the study of nonplanar traveling wave solutions of reaction–diffusion equations. In this paper, we study the pyramidal traveling fronts of nonlocal delayed diffusion equation in RN with N≥2 by using the comparison principle and establishing super- and subsolution. Since the effect of nonlocal delay, we show that nonlocal delayed diffusion equation in N-dimensional space has a pyramidal traveling front u(t,x)=V(x′,xN+st) toward XN-axis for each s>c>0. In particular, two-dimensional traveling curved front and three-dimensional pyramidal fronts for nonlocal delayed diffusion equation in R2 and R3 are also established, respectively. Moreover, we also extend our results to generally nonlocal delayed reaction–diffusion equation.
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