Parametrizations of sub-attractors in hyperbolic balance laws (Q2895828)
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scientific article; zbMATH DE number 6053146
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Parametrizations of sub-attractors in hyperbolic balance laws |
scientific article; zbMATH DE number 6053146 |
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Parametrizations of sub-attractors in hyperbolic balance laws (English)
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4 July 2012
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global attractor
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scalar balance law
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source term
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periodic boundary conditions
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heteroclinic orbits between different waves
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0.8725173
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0.8671945
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0.8667615
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0.8618608
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0.8606734
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0.8585984
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The article provides another step towards the description of the global attractor of a scalar balance law \(u_t+f(u)_x=g(u)\) on the circle. For a convex flux \(f\) this attractor is in general infinite-dimensional and consists of stationary solutions, rotating waves and heteroclinic connections between those objects. Ehrt focusses on finite-dimensional parts consisting of stationary states and waves with at most \(\alpha\) zeros together with connecting orbits between them. Apart from proving that the dimension of this subattractor is \(2\alpha\) she is able to characterize the heteroclinic orbits between different waves. As an illustration the subattractors for \(\alpha=1\) and \(\alpha=2\) with their internal dynamics are described in detail.
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