Uniqueness and existence of traveling waves for discrete quasilinear monostable dynamics
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We study traveling waves of a discrete system
where f and g are Lipschitz continuous with g increasing and f monostable, i.e., f(0)=f(1)=0 and f>0 on (0,1). We show that there is a positive cmin such that a traveling wave of speed c exists if and only if c≥cmin. Also, we show that traveling waves are unique up to a translation if f′(0)>0>f′(1) and g′(0)>0. The tails of traveling waves are also investigated.
KeywordsDiscrete System Monostable Dynamic
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© Springer-Verlag Berlin Heidelberg 2003