Hostname: page-component-7dd5485656-wlg5v Total loading time: 0 Render date: 2025-10-29T19:29:19.871Z Has data issue: false hasContentIssue false
  • English
  • Français

Wave solutions for a discrete reaction-diffusion equation

Published online by Cambridge University Press:  23 October 2000

A. CARPIO ,
S. J. CHAPMAN ,
S. HASTINGS  and
J. B. McLEOD
A. CARPIO
Affiliation:
Department of Applied Mathematics, Universidad Complutense de Madrid, Madrid, Spain
S. J. CHAPMAN
Affiliation:
Mathematical Institute , 24–29 St. Giles, Oxford OX1 3LB, UK
S. HASTINGS
Affiliation:
Department of Mathematics, University of Pittsburgh, PA, USA
J. B. McLEOD
Affiliation:
Department of Mathematics, University of Pittsburgh, PA, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

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

formula here

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.

Information

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 11 , Issue 4 , September 2000 , pp. 399 - 412
Copyright
2000 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable