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Parametrizations of sub-attractors in hyperbolic balance laws

Published online by Cambridge University Press:  07 June 2012

Julia Ehrt
Julia Ehrt
Affiliation:
Institut für Mathematik, Humboldt-Universität zu Berlin, Unter den Linden 6, 10099 Berlin, Germany (ehrt@math.hu-berlin.de)
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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
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 142 , Issue 3 , June 2012 , pp. 563 - 583
Copyright
Copyright © Royal Society of Edinburgh 2012

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