This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
D. Aregba-Driollet, M. Briani, R. Natalini, Asymptotic high-order schemes for dissipative hyperbolic systems, in preparation.
S. Bianchini, B. Hanouzet, R. Natalini, Asymptotic behavior of smooth solutions for partially dissipative hyperbolic systems with a convex entropy, IAC Report 79 (11/2005); to appear in Comm. Pure and Appl. Math.
G. Carbou, B. Hanouzet, Comportement semi-linaire d’un systme hyperbolique quasi-linaire: le modle de Kerr-Debye. (French) [Semilinear behavior for a quasilinear hyperbolic system: the Kerr-Debye model] C. R. Math. Acad. Sci. Paris 343 (2006), no. 4, 243–247.
G. Carbou, B. Hanouzet, Relaxation approximation of some nonlinear Maxwell initial-boundary value problem. Commun. Math. Sci. 4 (2006), no. 2, 331–344.
G.-Q. Chen, C.D. Levermore, and T.-P. Liu, Hyperbolic conservation laws with stiff relaxation terms and entropy, Comm. Pure and Appl. Math. 47 (1994), 787–830.
I.L. Chern, Long-time effect of relaxation for hyperbolic conservation laws, Commun. Math. Phys. 172 (1995), 39–55.
J.-F. Coulombel and T. Goudon, The strong relaxation limit of the multidimensional isothermal Euler equations, preprint 2004, to appear in Trans. AMS.
C.M. Dafermos, Hyperbolic conservation laws in continuum physics, (Springer-Verlag, Berlin, 2000) xvi+443 pp.
K.O. Friedrichs and P.D. Lax, Systems of conservation equations with a convex extension, Proc. Nat. Acad. Sci. U.S.A. 68 (1971), 1686–1688.
S.K. Godunov, An interesting class of quasi-linear systems, Dokl. Akad. Nauk SSSR 139 (1961), 521–523.
B. Hanouzet and Ph. Huynh, Approximation par relaxation d’un système de Maxwell non linéaire, C. R. Acad. Sci. Paris Sér. I Math. 330 (2000), no. 3, 193–198.
B. Hanouzet and R. Natalini, Global existence of smooth solutions for partially dissipative hyperbolic systems with a convex entropy, Arch. Ration. Mech. Anal. 169 (2003), no. 2, 89–117.
S. Kawashima, Large-time behaviour of solutions to hyperbolic-parabolic systems of conservation laws and applications, Proc. Roy. Soc. Edinburgh Sect. A 106 (1987), no. 1-2, 169–194.
T.-P. Liu, Hyperbolic conservation laws with relaxation, Comm. Math. Phys. 108 (1987), 153–175.
R. Natalini, Recent results on hyperbolic relaxation problems, Analysis of systems of conservation laws (Aachen, 1997), Chapman & Hall/CRC, Boca Raton, FL, 1999, pp. 128–198.
T. Nishida, Nonlinear hyperbolic equations and related topics in fluid dynamics, Département de Mathématique, Université de Paris-Sud, Orsay, 1978, Publications Mathématiques d’Orsay, No. 78-02.
T. Ruggeri and D. Serre, Stability of constant equilibrium state for dissipative balance laws system with a convex entropy. Quart. Appl. Math. 62 (2004), no. 1, 163–179.
Y. Shizuta and S. Kawashima, Systems of equations of hyperbolic-parabolic type with applications to the discrete Boltzmann equation, Hokkaido Math. J. 14 (1985), no. 2, 249–275.
T. Sideris, B. Thomases, and D. Wang, Decay and singularities of solutions of the three-dimensional Euler equations with damping, Comm. Partial Differential Equations 28 (2003), no. 3-4, 795–816.
W.-A. Yong, Entropy and global existence for hyperbolic balance laws, Arch. Ration. Mech. Anal. 172 (2004), no. 2, 247–266.
Y. Zeng, Gas dynamics in thermal nonequilibrium and general hyperbolic systems with relaxation, Arch. Ration. Mech. Anal. 150 (1999), no. 3, 225–279.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bianchini, S., Hanouzet, B., Natalini, R. (2008). Dissipative Hyperbolic Systems: the Asymptotic Behavior of Solutions. In: Benzoni-Gavage, S., Serre, D. (eds) Hyperbolic Problems: Theory, Numerics, Applications. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75712-2_5
Download citation
DOI: https://doi.org/10.1007/978-3-540-75712-2_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-75711-5
Online ISBN: 978-3-540-75712-2
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)