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Zbl 1116.35063
Guo, Jong-Shenq; Hamel, François
Front propagation for discrete periodic monostable equations. (English)
[J] Math. Ann. 335, No. 3, 489-525 (2006). ISSN 0025-5831; ISSN 1432-1807/e

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.
[Sen-Zhong Huang (Hamburg)]

MSC 2000:: *35K57 Reaction-diffusion equations
35K50 Systems of parabolic equations, boundary value problems
39A12 Discrete version of topics in analysis

Keywords: travelling wave solutions; minimal wave speed; pulsating traveling front

Cited in: Zbl 1195.34118

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