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Wave solutions for a discrete reaction-diffusion equation

  • A. CARPIO (a1), S. J. CHAPMAN (a2), S. HASTINGS (a3) and J. B. McLEOD (a3)
    • Published online: 23 October 2000
Abstract

Motivated by models from fracture mechanics and from biology, we study the infinite system of differential equations

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where A and F are positive parameters. For fixed A > 0 we show that there are monotone travelling waves for F in an interval Fcrit < F < A, and we are able to give a rigorous upper bound for Fcrit, in contrast to previous work on similar problems. We raise the problem of characterizing those nonlinearities (apparently the more common) for which Fcrit > 0. We show that, for the sine nonlinearity, this is true if A > 2. (Our method yields better estimates than this, but does not include all A > 0.) We also consider the existence and multiplicity of time independent solutions when |F|< Fcrit.

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European Journal of Applied Mathematics
  • ISSN: 0956-7925
  • EISSN: 1469-4425
  • URL: /core/journals/european-journal-of-applied-mathematics
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