WIAS Preprint No. 1518, (2010)

Parameterizations of sub-attractors in hyperbolic balance laws



Authors

  • Ehrt, Julia

2010 Mathematics Subject Classification

  • 35L60 35B41

2008 Physics and Astronomy Classification Scheme

  • 02.30.Jr

Keywords

  • global attractors, dissipative PDEs, sub-attractors

Abstract

This article investigates the properties of the global attractor of hyperbolic balance laws on the circle, given by : u_t+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 article proves finite dimensionality of all sub-attractors, provides a full parameterization of all sub-attractors and derives a system of ODEs for the embedding parameters that describes the full PDE dynamics on the sub-attractor.

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