BIANCHINI, Stefano; HANOUZET, Bernard; NATALINI, Roberto

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BIANCHINI, Stefano
istituto per le applicazioni del calculo [IAC]

HANOUZET, Bernard
Institut de Mathématiques de Bordeaux [IMB]

NATALINI, Roberto
istituto per le applicazioni del calculo [IAC]

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Communications on Pure and Applied Mathematics. 2007, vol. 60, n° 11, p. 1559-1622

Wiley

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We study the asymptotic time behavior of global smooth solutions to general entropy dissipative hyperbolic systems of balance law in m space dimensions, under the Shizuta-Kawashima condition. We show that these solutions approach constant equilibrium state in the Lp-norm at a rate O(t^(-m/2(1-1/p))), as t tends to $\infty$, for p in [min ( m,2),+ \infty]. Moreover, we can show that we can approximate, with a faster order of convergence, theconservative part of the solution in terms of the linearized hyperbolic operator for m >= 2, and by a parabolic equation in the spirit of Chapman-Enskog expansion. The main tool is given by a detailed analysis of the Green function for the linearized problem.< Réduire

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

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