TRANSITION FRONTS IN NONLOCAL EQUATIONS WITH TIME HETEROGENEOUS IGNITION NONLINEARITY

被引:9
作者
Shen, Wenxian [1 ]
Shen, Zhongwei [1 ,2 ]
机构
[1] Auburn Univ, Dept Math & Stat, Auburn, AL 36849 USA
[2] Univ Alberta, Dept Math & Stat Sci, Edmonton, AB T6G 2G1, Canada
关键词
Transition front; nonlocal equation; ignition nonlinearity; REACTION-DIFFUSION EQUATIONS; GENERALIZED TRAVELING-WAVES; SPACE PERIODIC HABITATS; SPREADING SPEEDS; MONOSTABLE EQUATIONS; EVOLUTION SYSTEMS; KPP EQUATIONS; PROPAGATION; MEDIA; UNIQUENESS;
D O I
10.3934/dcds.2017042
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
The present paper is devoted to the study of transition fronts in nonlocal reaction-diffusion equations with time heterogeneous nonlinearity of ignition type. It is proven that such an equation admits space monotone transition fronts with finite speed and space regularity in the sense of uniform Lipschitz continuity. Our approach is first constructing a sequence of approximating front-like solutions and then proving that the approximating solutions converge to a transition front. We take advantage of the idea of modified interface location, which allows us to characterize the finite speed of approximating solutions in the absence of space regularity, and leads directly to uniform exponential decaying estimates.
引用
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页码:1013 / 1037
页数:25
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