A locally contractive metric for systems of conservation laws

Alberto Bressan

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1995)

  • Volume: 22, Issue: 1, page 109-135
  • ISSN: 0391-173X

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Bressan, Alberto. "A locally contractive metric for systems of conservation laws." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 22.1 (1995): 109-135. <http://eudml.org/doc/84195>.

@article{Bressan1995,
author = {Bressan, Alberto},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {weighted norms},
language = {eng},
number = {1},
pages = {109-135},
publisher = {Scuola normale superiore},
title = {A locally contractive metric for systems of conservation laws},
url = {http://eudml.org/doc/84195},
volume = {22},
year = {1995},
}

TY - JOUR
AU - Bressan, Alberto
TI - A locally contractive metric for systems of conservation laws
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1995
PB - Scuola normale superiore
VL - 22
IS - 1
SP - 109
EP - 135
LA - eng
KW - weighted norms
UR - http://eudml.org/doc/84195
ER -

References

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  1. [1] A. Bressan, Contractive metrics for nonlinear hyperbolic systems. Indiana Univ. Math. J.37 (1988), 409-421. Zbl0632.35041MR963510
  2. [2] A. Bressan, A contractive metric for systems of conservation laws with coinciding shock and rarefaction waves. J. Differential Equations106 (1993), 332-366. Zbl0802.35095MR1251857
  3. [3] A. Bressan - A. Marson, A variational calculus for discontinuous solutions of systems of conservation laws. Preprint S.I.S.S.A., 1993. Zbl0846.35080
  4. [4] A. Bressan - G. Colombo, Existence and continuous dependence for discontinuous O.D.E's. Boll. Un. Mat. Ital.4-B (1990), 295-311. Zbl0709.34003MR1061219
  5. [5] A. Bressan - R.M. Colombo, The semigroup generated by 2 X 2 conservation laws. Arch. Rational Mech. Anal., submitted. Zbl0849.35068
  6. [6] R. Diperna, Uniqueness of solutions to hyperbolic conservation laws. Indiana Univ. Math. J.28 (1979), 137-188. Zbl0409.35057MR523630
  7. [7] J. Glimm, Solutions in the large for nonlinear hyperbolic systems of equations. Comm. Pure Appl. Math.18 (1965), 697-715. Zbl0141.28902MR194770
  8. [8] P. Lax, Hyperbolic systems of conservation laws II. Comm. Pure Appl. Math.10 (1957), 537-566. Zbl0081.08803MR93653
  9. [9] T.P. Liu, Uniqueness of weak solutions of the Cauchy problem for general 2 × 2 conservation laws. J. Differential Equations20 (1976), 369-388. Zbl0288.76031MR393871
  10. [10] T.P. Liu, Nonlinear stability of shock waves for viscous conservation laws. Mem. Amer. Math. Soc.328 (1985). Zbl0617.35058MR791863
  11. [11] V.J. Ljapidevskii, On correctness classes for nonlinear hyperbolic systems. Soviet Math. Dokl.16 (1975), 1505-1509. Zbl0329.35042MR407464
  12. [12] O. Oleinik, Uniqueness and stability of the generalized solution of the Cauchy problem for a quasilinear equation. Amer. Math. Soc. Transl. Ser.2, 33 (1963), 285-290. Zbl0132.33303
  13. [13] G. Pimbley, A semigroup for Lagrangian 1D isentropic flow. In "Transport theory, invariant imbedding and integral equations", G. Webb ed., M. Dekker, New York, 1989. Zbl0689.76003MR1023166
  14. [14] M. Schatzman, Continuous Glimm functionals and uniqueness of solutions of the Riemann problem. Indiana Univ. Math. J.34 (1985), 533-589. Zbl0579.35053MR794576
  15. [15] J. Smoller, Shock Waves and Reaction-Diffusion Equations, Springer-Verlag, New York, 1983. Zbl0508.35002MR688146
  16. [16] A. Szepessy - Z.P. Xin, Nonlinear stability of viscous shock waves. Arch. Rational Mech. Anal.122 (1993), 53-103. Zbl0803.35097MR1207241
  17. [17] B. Temple, No L1-contractive metrics for systems of conservation laws. Trans. Amer. Math. Soc.288 (1985), 471-480. Zbl0568.35065MR776388

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