A locally contractive metric for systems of conservation laws
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 22 (1995) no. 1, p. 109-135
@article{ASNSP_1995_4_22_1_109_0,
     author = {Bressan, Alberto},
     title = {A locally contractive metric for systems of conservation laws},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 22},
     number = {1},
     year = {1995},
     pages = {109-135},
     zbl = {0867.35060},
     mrnumber = {1315352},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_1995_4_22_1_109_0}
}
Bressan, Alberto. A locally contractive metric for systems of conservation laws. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 22 (1995) no. 1, pp. 109-135. http://www.numdam.org/item/ASNSP_1995_4_22_1_109_0/

[1] A. Bressan, Contractive metrics for nonlinear hyperbolic systems. Indiana Univ. Math. J. 37 (1988), 409-421. | MR 963510 | Zbl 0632.35041

[2] A. Bressan, A contractive metric for systems of conservation laws with coinciding shock and rarefaction waves. J. Differential Equations 106 (1993), 332-366. | MR 1251857 | Zbl 0802.35095

[3] A. Bressan - A. Marson, A variational calculus for discontinuous solutions of systems of conservation laws. Preprint S.I.S.S.A., 1993.

[4] A. Bressan - G. Colombo, Existence and continuous dependence for discontinuous O.D.E's. Boll. Un. Mat. Ital. 4-B (1990), 295-311. | MR 1061219 | Zbl 0709.34003

[5] A. Bressan - R.M. Colombo, The semigroup generated by 2 X 2 conservation laws. Arch. Rational Mech. Anal., submitted. | Zbl 0849.35068

[6] R. Diperna, Uniqueness of solutions to hyperbolic conservation laws. Indiana Univ. Math. J. 28 (1979), 137-188. | MR 523630 | Zbl 0409.35057

[7] J. Glimm, Solutions in the large for nonlinear hyperbolic systems of equations. Comm. Pure Appl. Math. 18 (1965), 697-715. | MR 194770 | Zbl 0141.28902

[8] P. Lax, Hyperbolic systems of conservation laws II. Comm. Pure Appl. Math. 10 (1957), 537-566. | MR 93653 | Zbl 0081.08803

[9] T.P. Liu, Uniqueness of weak solutions of the Cauchy problem for general 2 × 2 conservation laws. J. Differential Equations 20 (1976), 369-388. | MR 393871 | Zbl 0288.76031

[10] T.P. Liu, Nonlinear stability of shock waves for viscous conservation laws. Mem. Amer. Math. Soc. 328 (1985). | MR 791863 | Zbl 0617.35058

[11] V.J. Ljapidevskii, On correctness classes for nonlinear hyperbolic systems. Soviet Math. Dokl. 16 (1975), 1505-1509. | MR 407464 | Zbl 0329.35042

[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. | Zbl 0132.33303

[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. | MR 1023166 | Zbl 0689.76003

[14] M. Schatzman, Continuous Glimm functionals and uniqueness of solutions of the Riemann problem. Indiana Univ. Math. J. 34 (1985), 533-589. | MR 794576 | Zbl 0579.35053

[15] J. Smoller, Shock Waves and Reaction-Diffusion Equations, Springer-Verlag, New York, 1983. | MR 688146 | Zbl 0508.35002

[16] A. Szepessy - Z.P. Xin, Nonlinear stability of viscous shock waves. Arch. Rational Mech. Anal. 122 (1993), 53-103. | MR 1207241 | Zbl 0803.35097

[17] B. Temple, No L1-contractive metrics for systems of conservation laws. Trans. Amer. Math. Soc. 288 (1985), 471-480. | MR 776388 | Zbl 0568.35065