Nonlinear hyperbolic-dissipative partial differential equations

[Chen-Levermore-Liu], Chen, G.-Q., Levermore, D., and Liu, T.-P., Hyperbolic conservation laws with stiff relaxation terms and entropy. Comm. Pure Appl. Math. (1994).
Google Scholar
[Chern], Chern, I.-L., Multiple-mode diffusion waves for viscous nonstrictly hyperbolic conservation laws, Comm. Math. Phys., 138 (1991) 51–61.
Article MathSciNet MATH Google Scholar
[Freistuhler-Liu], Freistuhler, H., and Liu, T.-P., Nonlinear stability of overcompressive shock waves in a rotational invariant system of viscous conservation laws, Comm. Math. Phys., 153 (1993) 147–158.
Article MathSciNet MATH Google Scholar
[Fricket-Davis], Fricket, W. and Davis, W.C., Detonations, University of California Press, Berkeley, 1979.
Google Scholar
[Kawashima], Kawashima, K., Large-time behavior of solutions to hyperbolic-parabolic systems of conservation laws and applications, Proc. Roy. Soc. Edinburgh 106A (1987) 169–194.
Article MathSciNet MATH Google Scholar
[Lax], Lax, P.D., Hyperbolic System of Conservation Laws and the Mathematical Theory of Shock Waves, SIAM, Philadelphia, 1973.
Book MATH Google Scholar
[Liu 1], Liu, T.-P., Hyperbolic conservation laws with relaxation, Comm. Math. Phys. 108 (1987) 153–175.
Article MathSciNet MATH Google Scholar
[Liu 2], Liu, T.-P., Nonlinear hyperbolic-parabolic partial differential equations, Nonlinear Analysis, Proceedings, 1989 Conference. Liu, F.-C., and Liu, T.-P., (eds.), pp. 161–170. Academia Sinica, Taipei, R.O.C.; World Scientific.
Google Scholar
[Liu 3], Liu, T.-P., Pointwise convergence to shock waves for the system of viscous conservation laws, (to appear.)
Google Scholar
[Liu 4], Liu, T.-P., Interaction of nonlinear hyperbolic waves, Nonlinear Analysis, Proceedings, 1989 Conference, Liu, F.-C., and Liu, T.-P., (eds), pp. 171–184. Academia Sinica, Taipei, R.O.C.; World Scientific.
Google Scholar
[Liu 5], Liu, T.-P., The Riemann problem for viscous conservation laws, (to appear).
Google Scholar
[Liu-Zeng], Liu, T.-P., Large time behaviour of solutions for general quasilinear hyperbolic-parabolic systems of conservation laws, (preprint.)
Google Scholar
[Liu-Zumbrun], Liu, T.-P., and Zumbrun, K., On nonlinear stability of general undercompressive viscous shock waves, (preprint.)
Google Scholar
[Szepessy-Zumbrun], A. Szepessy, and Zumbrun, K., Stability of viscous conservation laws, Archive Rational Mech. Anal. (to appear.)
Google Scholar
[Whitham], Whitham, J. Linear and Nonlinear Waves, New York: Wiley 1974.
MATH Google Scholar

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Department of Mathematics, Stanford University, USA
Tai-Ping Liu

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Tai-Ping Liu
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Tommaso Ruggeri

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Liu, TP. (1996). Nonlinear hyperbolic-dissipative partial differential equations. In: Ruggeri, T. (eds) Recent Mathematical Methods in Nonlinear Wave Propagation. Lecture Notes in Mathematics, vol 1640. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0093708

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DOI: https://doi.org/10.1007/BFb0093708
Published: 13 October 2006
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-61907-9
Online ISBN: 978-3-540-49565-9
eBook Packages: Springer Book Archive

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Nonlinear hyperbolic-dissipative partial differential equations

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