Journal of Dynamics and Differential Equations

, Volume 5, Issue 2, pp 359–373

Wavefronts for a cooperative tridiagonal system of differential equations

  • D. Hankerson
  • B. Zinner
Article

DOI: 10.1007/BF01053165

Cite this article as:
Hankerson, D. & Zinner, B. J Dyn Diff Equat (1993) 5: 359. doi:10.1007/BF01053165

Abstract

Consider the infinite system of nonlinear differential equations\(\dot u\)n =f(n−1, un, un+1),nεℤ, wherefεC1,D1f > 0,D3f>0, andf(0, 0, 0) = 0 =f(1, 1, 1). Existence of wavefronts—i.e., solutions of the formun(t) = U(n + ct), whereℝ,U(− ∞) = 0,U(+∞) = 1, andU is strictly increasing—is shown for functionsf which satisfy the condition: there existsa, 0<a<1, such thatf(x, x,x)<0 for 0<x<a andf(x, x, x) > 0 fora < x < 1.

Key words

Traveling waves Nagumo equation cooperative systems comparision principles 

Copyright information

© Plenum Publishing Corporation 1993

Authors and Affiliations

  • D. Hankerson
    • 1
  • B. Zinner
    • 1
  1. 1.Department of Discrete and Statistical SciencesAuburn UniversityAuburn