Viscous Limits for strong shocks of one-dimensional systems of conservation laws

Frédéric Rousset

Journées équations aux dérivées partielles (2002)

  • page 1-11
  • ISSN: 0752-0360

Abstract

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We consider a piecewise smooth solution of a one-dimensional hyperbolic system of conservation laws with a single noncharacteristic Lax shock. We show that it is a zero dissipation limit assuming that there exist linearly stable viscous profiles associated with the discontinuities. In particular, following the approach of Grenier and Rousset (2001), we replace the smallness condition obtained by energy methods in Goodman and Xin (1992) by a weaker spectral assumption.

How to cite

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Rousset, Frédéric. "Viscous Limits for strong shocks of one-dimensional systems of conservation laws." Journées équations aux dérivées partielles (2002): 1-11. <http://eudml.org/doc/93427>.

@article{Rousset2002,
abstract = {We consider a piecewise smooth solution of a one-dimensional hyperbolic system of conservation laws with a single noncharacteristic Lax shock. We show that it is a zero dissipation limit assuming that there exist linearly stable viscous profiles associated with the discontinuities. In particular, following the approach of Grenier and Rousset (2001), we replace the smallness condition obtained by energy methods in Goodman and Xin (1992) by a weaker spectral assumption.},
author = {Rousset, Frédéric},
journal = {Journées équations aux dérivées partielles},
language = {eng},
pages = {1-11},
publisher = {Université de Nantes},
title = {Viscous Limits for strong shocks of one-dimensional systems of conservation laws},
url = {http://eudml.org/doc/93427},
year = {2002},
}

TY - JOUR
AU - Rousset, Frédéric
TI - Viscous Limits for strong shocks of one-dimensional systems of conservation laws
JO - Journées équations aux dérivées partielles
PY - 2002
PB - Université de Nantes
SP - 1
EP - 11
AB - We consider a piecewise smooth solution of a one-dimensional hyperbolic system of conservation laws with a single noncharacteristic Lax shock. We show that it is a zero dissipation limit assuming that there exist linearly stable viscous profiles associated with the discontinuities. In particular, following the approach of Grenier and Rousset (2001), we replace the smallness condition obtained by energy methods in Goodman and Xin (1992) by a weaker spectral assumption.
LA - eng
UR - http://eudml.org/doc/93427
ER -

References

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  14. [14] F. Rousset. Viscous limits for strong shocks of systems of conservation laws. Preprint, 2001 XVI-11 
  15. [15] A. I. Volpert. Spaces BV and quasilinear equations. Mat. Sb.(N.S.), 73(115):255-302, 1967. Zbl0168.07402MR216338
  16. [16] S. H. Yu. Zero-dissipation limit of solutions with shocks for systems of hyperbolic conservation laws. Arch. Ration. Mech. Anal., 146(4):275-370, 1999. Zbl0935.35101MR1718368
  17. [17] K. Zumbrun and P. Howard. Pointwise semigroup methods and stability of viscous shock waves. Indiana Univ. Math. J., 47(3):741-871, 1998. Zbl0928.35018MR1665788
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