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Asymptotic behavior of smooth solutions for partially dissipative hyperbolic systems with a convex entropy (Articolo in rivista)

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Asymptotic behavior of smooth solutions for partially dissipative hyperbolic systems with a convex entropy (Articolo in rivista) (literal)

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Bianchini S.; Hanouzet B.; Natalini R. (2007)
Asymptotic behavior of smooth solutions for partially dissipative hyperbolic systems with a convex entropy
in Communications on pure and applied mathematics (Print); John Wiley & Sons Inc., Hoboken (Stati Uniti d'America)
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Titolo

Asymptotic behavior of smooth solutions for partially dissipative hyperbolic systems with a convex entropy (literal)

Abstract

We study the asymptotic time behavior of global smooth solutions to general entropy, dissipative, hyperbolic systems of balance laws in m space dimensions, under the Shizuta-Kawashima condition. We show that these solutions approach a constant equilibrium state in the L p -norm at a rate O(t -(m/2)(1-1/ p) ) as t -> ? for p ? [min{m, 2}, ?]. Moreover, we can show that we can approxi- mate, with a faster order of convergence, the conservative part of the solution in terms of the linearized hyperbolic operator for m >= 2, and by a parabolic equa- tion, in the spirit of Chapman-Enskog expansion in every space dimension. The main tool is given by a detailed analysis of the Green function for the linearized problem. (literal)

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