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Zbl 1155.34016
Guo, Jong-Shenq; Wu, Chang-Hong
Existence and uniqueness of traveling waves for a monostable 2-D lattice dynamical system. (English)
[J] Osaka J. Math. 45, No. 2, 327-346 (2008). ISSN 0030-6126

The authors study the existence and uniqueness of traveling waves of a two-dimensional lattice differential equation, which can be regarded as a spatial discrete version of a reaction-diffusion equation. In the case of a monostable nonlinearity it is shown that there is a minimal wave speed such that traveling waves exist if and only if its speed is larger than the minimal one. Moreover, it is proved that given any admissable wave speed the corresponding wave profile is unique up to translation. As techniques the authors use the monotone iteration method.
[Marc Georgi (Berlin)]

MSC 2000:: *34B40 Boundary value problems on infinite intervals
34A35 ODE of infinite order

Keywords: traveling waves; minimal wave speed; two-dimensional lattice differential equation; monotone iteration method

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