具有双稳非线性项的非局部时滞扩散方程的柱状对称波前解

Cylindrically Symmetric Traveling Fronts for Nonlocal Delayed Diffusion Equation with Bistable Nonlinearity

本文研究了非局部时滞扩散方程柱状对称波前解的存在性和定性性质.最近,非局部时滞扩散方程的V形行波解和棱锥形行波解已经有了研究结果.利用棱锥形波前解序列的极限,我们建立了柱状对称波前解的存在性和定性性质,也证明了其水平集的渐近行为和柱状对称行波解的不存在性.

This paper is concerned with the existence and qualitative properties of cylindrically symmetric traveling fronts for nonlocal delayed diffusion equations.Recently,the existence and stability of V-shaped traveling fronts and pyramidal traveling fronts for nonlocal delayed diffusion equation have been established.Using the limit of a sequence of pyramidal traveling fronts,we establish the existence and qualitative properties of cylindrically symmetric traveling fronts.Moreover,the asymptotic behaviors of level set and the nonexistence of the cylindric symmetric traveling are also proved.