Global Stability of Monostable Traveling Waves For Nonlocal Time-Delayed Reaction-Diffusion Equations
Global Stability of Monostable Traveling Waves For Nonlocal Time-Delayed Reaction-Diffusion Equations
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DOI：
10.1137/090776342
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发表时间：
2010-11
期刊：
影响因子：
--
通讯作者：
Ming Mei;Chunhua Ou;Xiao-Qiang Zhao
中科院分区：
文献类型：
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作者：
Ming Mei;Chunhua Ou;Xiao-Qiang Zhao
对于一类非局部时滞反应扩散方程，证明了所有非临界波前都是全局指数稳定的，而当波前附近的初始扰动在负无穷大附近指数衰减到零时，临界波前是全局代数稳定的，与时滞的大小无关.本文的工作也改进和发展了已有的局部和非局部时滞反应扩散方程的稳定性结果。我们的方法是基于加权能量法和绿色函数技术相结合。
For a class of nonlocal time-delayed reaction-diffusion equations, we prove that all noncritical wavefronts are globally exponentially stable, and critical wavefronts are globally algebraically stable when the initial perturbations around the wavefront decay to zero exponentially near the negative infinity regardless of the magnitude of time delay. This work also improves and develops the existing stability results for local and nonlocal reaction-diffusion equations with delays. Our approach is based on the combination of the weighted energy method and the Green function technique.