Hostname: page-component-848d4c4894-jbqgn Total loading time: 0 Render date: 2024-07-03T22:56:25.090Z Has data issue: false hasContentIssue false

Parametrizations of sub-attractors in hyperbolic balance laws

Published online by Cambridge University Press:  07 June 2012

Julia Ehrt
Affiliation:
Institut für Mathematik, Humboldt-Universität zu Berlin, Unter den Linden 6, 10099 Berlin, Germany (ehrt@math.hu-berlin.de)

Abstract

We investigate the properties of the global attractor of hyperbolic balance laws on the circle, given by

ut + f(u)x = g(u).

The new tool of sub-attractors is introduced. They contain all solutions on the global attractor up to a given number of zeros. The paper proves finite dimensionality of all sub-attractors, provides a full parametrization of all sub-attractors and derives a system of ordinary differential equations for the embedding parameters that describe the full partial differential equation dynamics on the sub-attractor.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 2012

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.)