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Front propagation for discrete periodic monostable equations. (English) Zbl 1116.35063
The systems of infinitely many ordinary differential equations (ODEs) under study arise from the spatial-discrete version of a one-dimensional continuous periodic reaction-diffusion equation. The authors show that pulsating travelling solutions to the ODE systems exist if and only if the wave speed of the solutions is above some minimal level. Moreover, the authors prove that the minimal speed levels for the spatial-discrete version converge in some appropriate sense to the minimal speed level for the existence of pulsating traveling solutions to the continuous version.

MSC:
35K57Reaction-diffusion equations
35K50Systems of parabolic equations, boundary value problems (MSC2000)
39A12Discrete version of topics in analysis
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