On the well posedness of vanishing viscosity limits

Alberto Bressan

Journées équations aux dérivées partielles (2002)

  • page 1-10
  • ISSN: 0752-0360

Abstract

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This paper provides a survey of recent results concerning the stability and convergence of viscous approximations, for a strictly hyperbolic system of conservation laws in one space dimension. In the case of initial data with small total variation, the vanishing viscosity limit is well defined. It yields the unique entropy weak solution to the corresponding hyperbolic system.

How to cite

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Bressan, Alberto. "On the well posedness of vanishing viscosity limits." Journées équations aux dérivées partielles (2002): 1-10. <http://eudml.org/doc/93431>.

@article{Bressan2002,
abstract = {This paper provides a survey of recent results concerning the stability and convergence of viscous approximations, for a strictly hyperbolic system of conservation laws in one space dimension. In the case of initial data with small total variation, the vanishing viscosity limit is well defined. It yields the unique entropy weak solution to the corresponding hyperbolic system.},
author = {Bressan, Alberto},
journal = {Journées équations aux dérivées partielles},
language = {eng},
pages = {1-10},
publisher = {Université de Nantes},
title = {On the well posedness of vanishing viscosity limits},
url = {http://eudml.org/doc/93431},
year = {2002},
}

TY - JOUR
AU - Bressan, Alberto
TI - On the well posedness of vanishing viscosity limits
JO - Journées équations aux dérivées partielles
PY - 2002
PB - Université de Nantes
SP - 1
EP - 10
AB - This paper provides a survey of recent results concerning the stability and convergence of viscous approximations, for a strictly hyperbolic system of conservation laws in one space dimension. In the case of initial data with small total variation, the vanishing viscosity limit is well defined. It yields the unique entropy weak solution to the corresponding hyperbolic system.
LA - eng
UR - http://eudml.org/doc/93431
ER -

References

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  4. [B3] A. Bressan, Hyperbolic Systems of Conservation Laws. The One Dimensional Cauchy Problem. Oxford University Press, 2000. Zbl0997.35002MR1816648
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  6. [BLY] A. Bressan, T. P. Liu and T. Yang, L 1 stability estimates for n Ã— n conservation laws, Arch. Rational Mech. Anal. 149 (1999), 1-22. Zbl0938.35093MR1723032
  7. [BS] A. Bressan and W. Shen, Uniqueness for discontinuous O.D.E. and conservation laws, Nonlinear Analysis, T. M. A. 34 (1998), 637-652. Zbl0948.34006MR1634652
  8. [DP] R. DiPerna, Convergence of approximate solutions to conservation laws, Arch. Rational Mech. Anal. 82 (1983), 27-70. Zbl0519.35054MR684413
  9. [G] J. Glimm, Solutions in the large for nonlinear hyperbolic systems of equations, Comm. Pure Appl. Math. 18 (1965), 697-715. Zbl0141.28902MR194770
  10. [GX] J. Goodman and Z. Xin, Viscous limits for piecewise smooth solutions to systems of conservation laws, Arch. Rational Mech. Anal. 121 (1992), 235- 265. Zbl0792.35115MR1188982
  11. [K] S. Kruzhkov, First order quasilinear equations with several space variables, Math. USSR Sbornik 10 (1970), 217-243. Zbl0215.16203
  12. [J] H. K. Jenssen, Blowup for systems of conservation laws, SIAM J. Math. Anal. 31 (2000), 894-908. Zbl0969.35091MR1752421
  13. [L] T. P. Liu, Admissible solutions of hyperbolic conservation laws, Amer. Math. Soc. Memoir 240 (1981). Zbl0446.76058MR603391
  14. [O] O. Oleinik, Discontinuous solutions of nonlinear differential equations (1957), Amer. Math. Soc. Translations 26, 95-172. Zbl0131.31803MR151737
  15. [V] A. Vanderbauwhede, Centre manifolds, normal forms and elementary bifurcations, Dynamics Reported, Vol. 2 (1989 Zbl0677.58001MR1000977

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