# On the well posedness of vanishing viscosity limits

Journées équations aux dérivées partielles (2002)

- page 1-10
- ISSN: 0752-0360

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topBressan, 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

top- [BB] S. Bianchini and A. Bressan, Vanishing viscosity solutions to nonlinear hyperbolic systems, Preprint S.I.S.S.A., Trieste 2001.
- [B1] A. Bressan, Unique solutions for a class of discontinuous differential equations, Proc. Amer. Math. Soc. 104 (1988), 772-778. Zbl0692.34004MR964856
- [B2] A. Bressan, The unique limit of the Glimm scheme, Arch. Rational Mech. Anal. 130 (1995), 205-230. IV-9 Zbl0835.35088MR1337114
- [B3] A. Bressan, Hyperbolic Systems of Conservation Laws. The One Dimensional Cauchy Problem. Oxford University Press, 2000. Zbl0997.35002MR1816648
- [BG] A. Bressan and P. Goatin, Oleinik type estimates and uniqueness for n x n conservation laws, J. Diff. Equat. 156 (1999), 26-49. Zbl0990.35095MR1701818
- [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
- [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
- [DP] R. DiPerna, Convergence of approximate solutions to conservation laws, Arch. Rational Mech. Anal. 82 (1983), 27-70. Zbl0519.35054MR684413
- [G] J. Glimm, Solutions in the large for nonlinear hyperbolic systems of equations, Comm. Pure Appl. Math. 18 (1965), 697-715. Zbl0141.28902MR194770
- [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
- [K] S. Kruzhkov, First order quasilinear equations with several space variables, Math. USSR Sbornik 10 (1970), 217-243. Zbl0215.16203
- [J] H. K. Jenssen, Blowup for systems of conservation laws, SIAM J. Math. Anal. 31 (2000), 894-908. Zbl0969.35091MR1752421
- [L] T. P. Liu, Admissible solutions of hyperbolic conservation laws, Amer. Math. Soc. Memoir 240 (1981). Zbl0446.76058MR603391
- [O] O. Oleinik, Discontinuous solutions of nonlinear differential equations (1957), Amer. Math. Soc. Translations 26, 95-172. Zbl0131.31803MR151737
- [V] A. Vanderbauwhede, Centre manifolds, normal forms and elementary bifurcations, Dynamics Reported, Vol. 2 (1989 Zbl0677.58001MR1000977

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