Parameterizations of sub-attractors in hyperbolic balance laws
- Ehrt, Julia
2010 Mathematics Subject Classification
- 35L60 35B41
2008 Physics and Astronomy Classification Scheme
- global attractors, dissipative PDEs, sub-attractors
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.