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Existence and uniqueness of traveling waves for a monostable 2-D lattice dynamical system. (English) Zbl 1155.34016
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.
MSC:
34B40Boundary value problems for ODE on infinite intervals
34A35ODE of infinite order