Generalized characteristics uniqueness and regularity of solutions in a hyperbolic system of conservation laws
Annales de l'I.H.P. Analyse non linéaire, Volume 8 (1991) no. 3-4, p. 231-269
@article{AIHPC_1991__8_3-4_231_0,
author = {Dafermos, C. M. and Geng, X.},
title = {Generalized characteristics uniqueness and regularity of solutions in a hyperbolic system of conservation laws},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
publisher = {Gauthier-Villars},
volume = {8},
number = {3-4},
year = {1991},
pages = {231-269},
zbl = {0776.35033},
mrnumber = {1127926},
language = {en},
url = {http://www.numdam.org/item/AIHPC_1991__8_3-4_231_0}
}

Dafermos, C. M.; Geng, X. Generalized characteristics uniqueness and regularity of solutions in a hyperbolic system of conservation laws. Annales de l'I.H.P. Analyse non linéaire, Volume 8 (1991) no. 3-4, pp. 231-269. http://www.numdam.org/item/AIHPC_1991__8_3-4_231_0/

[1] C.M. Dafermos, Characteristics in Hyperbolic Conservation Laws, Nonlinear Analysis and Mechanics, Vol. I, R. J. KNOPS Ed., London, Pitman, 1977, pp. 1-58. | MR 481581 | Zbl 0373.35048

[2] C.M. Dafermos, Generalized Characteristics and the Structure of Solutions of Hyperbolic Conservation Laws, Indiana Univ. Math. J., Vol. 26, 1977, pp. 1097-1119. | MR 457947 | Zbl 0377.35051

[3] C.M. Dafermos, Regularity and Large Time Behavior of Solutions of a Conservation Law Without Convexity, Proc. Roy. Soc. Edinb., Vol. 99 A, 1985, pp. 201-239. | MR 785530 | Zbl 0616.35054

[4] C.M. Dafermos, Dissipation in Materials With Memory, Viscoelasticity and Rheology, A. LODGE, J. A. NOHEL and M. RENARDY Eds., New York, Academic Press, 1985, pp. 221-234. | MR 830204 | Zbl 0588.73072

[5] C.M. Dafermos, Generalized Characteristics in Hyperbolic Systems of Conservation Laws, Arch. Rational Mech. Anal., Vol. 107, 1989, pp. 127-155. | MR 996908 | Zbl 0714.35046

[6] R.J. Diperna, Singularities of Solutions of Nonlinear Hyperbolic Systems of Conservation Laws, Arch. Rational Mech. Anal., Vol. 60, 1975, pp. 75-100. | MR 393867 | Zbl 0324.35062

[7] R.J. Diperna, Uniqueness of Solutions to Hyperbolic Conservation Laws, Indiana Univ. Math. J., Vol. 28, 1979, pp. 137-188. | MR 523630 | Zbl 0409.35057

[8] A.F. Filippov, Differential Equations with Discontinuous Right-Hand Side, Mat. Sb. (N.S.), Vol. 51, 1960, pp. 99-128. English transl., Am. Math. Soc. Transl., Ser. 2, Vol. 42, pp. 199-231. | MR 114016 | Zbl 0138.32204

[9] Xiao Geng, The Conservation Laws in Isotachophoresis Model (to appear).

[10] J. Glimm, Solution in the Large for Nonlinear Hyperbolic Systems of Equations, Comm. Pure Appl. Math., Vol. 18, 1965, pp. 697-715. | MR 194770 | Zbl 0141.28902

[11] A.E. Hurd, A Uniqueness Theorem for Weak Solutions of Symmetric Quasilinear Hyperbolic Systems, Pacific J. Math., Vol. 28, 1969, pp. 555-559. | MR 240454 | Zbl 0172.38305

[12] P.D. Lax, Hyperbolic systems of conservation laws II. Comm. Pure Appl. Math., Vol. 10, 1957, pp. 537-566. | MR 93653 | Zbl 0081.08803

[13] P.D. Lax, Shock Waves and Entropy, Contributions to Functional Analysis, E. A. ZARANTONELLO Ed., New York, Academic Press, 1971, pp. 603-634. | MR 393870 | Zbl 0268.35014

[14] R.J. Levesque and B. Temple, Stability of Godunov's Method for a Class of 2 × 2 Systems of Conservation Laws, Trans. Am. Math. Soc., Vol. 288, 1985, pp. 115-123. | MR 773050 | Zbl 0561.65067

[15] T.-P. Liu, Uniqueness of Weak Solutions of the Cauchy Problem for General 2 x 2 Conservation laws, J. Diff. Eqs., Vol. 20, 1976, pp. 369-388. | MR 393871 | Zbl 0288.76031

[16] O.A. Oleinik, Discontinuous Solutions of Nonlinear Differential Equations, Usp. Mat. Nauk (N.S.), Vol. 12, 1957, pp. 3-73. English Transl., Am. Math. Soc. Transl., Ser. 2, Vol. 26, pp. 95-172. | Zbl 0131.31803

[17] O.A. Oleinik, On the Uniqueness of the Generalized Solution of the Cauchy Problem for a Nonlinear System of Equations Occurring in Mechanics, Usp. Mat. Nauk (N.S.), Vol. 12, 1957, pp. 169-176. | MR 94543 | Zbl 0080.07702

[18] D.G. Schaeffer, A Regularity Theorem for Conservation Laws, Adv. in Math., Vol. 11, 1973, pp. 368-386. | MR 326178 | Zbl 0267.35009

[19] D. Serre, Solutions à variations bornées pour certains systèmes hyperboliques de lois de conservatian, J. Diff. Eqs., Vol. 68, 1987, pp. 137-169. | MR 892021 | Zbl 0627.35062

[20] B. Temple, Systems of Conservation Laws with Invariant Submanifolds, Trans. Am. Math. Soc., Vol. 280, 1983, pp. 781-795. | MR 716850 | Zbl 0559.35046