This paper is concerned with stability of traveling wave fronts for nonlocal diffusive system. We adopt L1-weighted, L1- and L2-energy estimates for the perturbation systems, and show that all solutions of the Cauchy problem for the considered systems converge exponentially to traveling wave fronts provided that the initial perturbations around the traveling wave fronts belong to a suitable weighted Sobolev spaces.

中文翻译：

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非局域扩散系统行波前的稳定性

本文关注的是非局域扩散系统行波阵面的稳定性。我们采用大号1-加权，大号1- 和大号2- 扰动系统的能量估计，并表明如果行波前周围的初始扰动属于合适的加权 Sobolev 空间，则所考虑系统的柯西问题的所有解都以指数方式收敛到行波前。