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Parameterizations of sub-attractors in hyperbolic balance laws
2010, Ehrt, Julia
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