GLOBAL STABILITY OF MONOSTABLE TRAVELING WAVES FOR NONLOCAL TIME-DELAYED REACTION-DIFFUSION EQUATIONS

被引：109
|
作者：
Mei, Ming [1 ]
Ou, Chunhua [2 ]
Zhao, Xiao-Qiang [2 ]
机构：
[1] Champlain Coll, Dept Math, St Lambert, PQ J4P 3P2, Canada
[2] Mem Univ Newfoundland, Dept Math & Stat, St John, NF A1C 5S7, Canada
来源：
SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2010年 / 42卷 / 06期
基金：
加拿大自然科学与工程研究理事会;
关键词：
nonlocal reaction-diffusion equations; time delays; traveling waves; global stability; the Fisher-KPP equation; L-1-weighted energy; Green functions; NICHOLSONS BLOWFLIES EQUATION; FUNCTIONAL-DIFFERENTIAL EQUATIONS; DISTRIBUTED MATURATION DELAY; VECTOR-DISEASE-MODEL; POPULATION-MODEL; ASYMPTOTIC STABILITY; LOCAL STABILITY; STAGE STRUCTURE; FRONTS; EXISTENCE;
D O I：
10.1137/090776342
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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.
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页码：2762 / 2790
页数：29
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