非局部时滞反应扩散方程行波解的稳定性

王小焕, 吕广迎

数学学报 ›› 2015, Vol. 58 ›› Issue (1) : 13-28.

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数学学报 ›› 2015, Vol. 58 ›› Issue (1) : 13-28. DOI: 10.12386/A2015sxxb0002
论文

非局部时滞反应扩散方程行波解的稳定性

    王小焕1, 吕广迎2
作者信息 +

Stability of Traveling Wave Fronts for Nonlocal Reaction Diffusion Equations with Delay

    Xiao Huan WANG1, Guang Ying LV2
Author information +
文章历史 +

摘要

考虑了非局部时滞反应扩散方程行波解的稳定性. 在合适的加权L空间下, 证明了非临界波指数稳定,临界波代数稳定(即代数衰减).还利用加权能量估计的方法得到了衰减速率.我们把相关结果应用到了host-vector模型, Nicholsonblowflies方程和一个修改了的传染病模型.

Abstract

This paper is concerned with the stability of traveling wave fronts for reaction diffusion equations with nonlocal delay. We prove that, in the appropriate weighted L spaces, the non-critical traveling wave fronts are globally exponentially stable, and the critical traveling wave fronts are globally algebraically stable. Moreover, we obtain the rates of convergence by weighted energy estimates. We apply these results to a host-vector disease model, the generalized Nicholson blowflies equation, and a modified vector disease model.

关键词

反应扩散方程 / 加权能量估计 / 行波解 / 稳定性 / 时滞

Key words

reaction diffusion equations / weighted energy estimate / traveling wave fronts / stability / delay

引用本文

导出引用
王小焕, 吕广迎. 非局部时滞反应扩散方程行波解的稳定性. 数学学报, 2015, 58(1): 13-28 https://doi.org/10.12386/A2015sxxb0002
Xiao Huan WANG, Guang Ying LV. Stability of Traveling Wave Fronts for Nonlocal Reaction Diffusion Equations with Delay. Acta Mathematica Sinica, Chinese Series, 2015, 58(1): 13-28 https://doi.org/10.12386/A2015sxxb0002

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基金

国家自然科学基金资助项目(11301146)

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