STABILITY, UNIQUENESS AND RECURRENCE OF GENERALIZED TRAVELING WAVES IN TIME HETEROGENEOUS MEDIA OF IGNITION TYPE

被引:26
|
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
Generalized traveling wave; stability; monotonicity; uniqueness; recurrence; almost periodicity; ASYMPTOTIC STABILITY; FRONT PROPAGATION; DIFFUSION; EXISTENCE; EQUATIONS; MODELS;
D O I
10.1090/tran/6726
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
The present paper is devoted to the study of stability, uniqueness and recurrence of generalized traveling waves of reaction-diffusion equations in time heterogeneous media of ignition type, whose existence has been proven by the authors of the present paper in a previous work. It is first shown that generalized traveling waves exponentially attract wave-like initial data. Next, properties of generalized traveling waves, such as space monotonicity and exponential decay ahead of interface, are obtained. Uniqueness up to space translations of generalized traveling waves is then proven. Finally, it is shown that the wave profile and the front propagation velocity of the unique generalized traveling wave are of the same recurrence as the media. In particular, if the media is time almost periodic, then so are the wave profile and the front propagation velocity of the unique generalized traveling wave.
引用
收藏
页码:2573 / 2613
页数:41
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