2000 A domain-wall between single-mode and bimodal states
G. J. B. van den Berg, R. C. A. M. van der Vorst
Differential Integral Equations 13(1-3): 369-400 (2000). DOI: 10.57262/die/1356124304


We examine a model equation describing spatial patterns in a class of physical systems where instabilities to travelling waves occur. The spatial patterns are modelled by a system of two second order ordinary differential equations, in which the cross-coupling coefficient is spatially dependent. The system has two clearly distinct types of stationary states, of which the stability depends on the cross-coupling coefficient. Under mild assumptions on the cross-coupling coefficient, we apply a variational method to prove the existence of a heteroclinic orbit between both types of states, corresponding to a domain-wall in the physical picture. This solution is found as a minimizer of a Lyapunov functional and the variational structure is exploited to obtain detailed information about the shape of the solution. In the case of a constant cross-coupling coefficient we find heteroclinic solutions connecting stationary states of the same type.


Download Citation

G. J. B. van den Berg. R. C. A. M. van der Vorst. "A domain-wall between single-mode and bimodal states." Differential Integral Equations 13 (1-3) 369 - 400, 2000. https://doi.org/10.57262/die/1356124304


Published: 2000
First available in Project Euclid: 21 December 2012

zbMATH: 1161.34322
MathSciNet: MR1811963
Digital Object Identifier: 10.57262/die/1356124304

Primary: 34B40
Secondary: 34B15 , 35K55 , 49J10

Rights: Copyright © 2000 Khayyam Publishing, Inc.


This article is only available to subscribers.
It is not available for individual sale.

Vol.13 • No. 1-3 • 2000
Back to Top