@article{AIHPC_1993__10_6_627_0, author = {Rubino, Bruno}, title = {On the vanishing viscosity approximation to the {Cauchy} problem for a 2 {\texttimes} 2 system of conservation laws}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {627--656}, publisher = {Gauthier-Villars}, volume = {10}, number = {6}, year = {1993}, mrnumber = {1253605}, zbl = {0806.35117}, language = {en}, url = {http://www.numdam.org/item/AIHPC_1993__10_6_627_0/} }
TY - JOUR AU - Rubino, Bruno TI - On the vanishing viscosity approximation to the Cauchy problem for a 2 × 2 system of conservation laws JO - Annales de l'I.H.P. Analyse non linéaire PY - 1993 SP - 627 EP - 656 VL - 10 IS - 6 PB - Gauthier-Villars UR - http://www.numdam.org/item/AIHPC_1993__10_6_627_0/ LA - en ID - AIHPC_1993__10_6_627_0 ER -
%0 Journal Article %A Rubino, Bruno %T On the vanishing viscosity approximation to the Cauchy problem for a 2 × 2 system of conservation laws %J Annales de l'I.H.P. Analyse non linéaire %D 1993 %P 627-656 %V 10 %N 6 %I Gauthier-Villars %U http://www.numdam.org/item/AIHPC_1993__10_6_627_0/ %G en %F AIHPC_1993__10_6_627_0
Rubino, Bruno. On the vanishing viscosity approximation to the Cauchy problem for a 2 × 2 system of conservation laws. Annales de l'I.H.P. Analyse non linéaire, Tome 10 (1993) no. 6, pp. 627-656. http://www.numdam.org/item/AIHPC_1993__10_6_627_0/
[1] Convergence of the Lax-Friedrichs Scheme for Isentropic Gas Dynamics, I, Acta Math. Sci., Vol. 5, 1985, pp. 415-432; II, Acta Math. Sci., Vol. 5, 1985, pp 433-472. | Zbl
, and ,[2] Convergence of the Lax-Friedrichs Scheme for Isentropic Gas Dynamics, III, Acta Math. Sci., Vol. 6, 1986, pp. 75-120. | Zbl
,[3] Positively Invariant Regions for Systems of Non-Linear Diffusion Equations, Indiana Univ. Math. J., Vol. 26, 1977, pp. 372-411. | Zbl
, and ,[4] Methods of Mathematicals Physics II: Partial Differential Equations, Wiley and Sons, 1962. | Zbl
and ,[5] Compensated Compactness and General Systems of Conservation Laws, Trans. Amer. Math. Soc., Vol. 292, 1985, pp. 383-420. | Zbl
,[6] Convergence of Approximate Solutions to Conservation Laws, Arch. Rational Mech. Anal., Vol. 82, 1983, pp. 27-70. | Zbl
,[7] Convergence of the Viscosity Method for Isentropic Gas Dynamics, Comm. Math. Phys., Vol. 91, 1983, pp. 1-30. | Zbl
,[8] Measure-Valued Solutions to Conservation Laws, Arch. Rational Mech. Anal., Vol. 88, 1985, pp. 223-270. | Zbl
,[9] Partial Differential Equations of Parabolic Type, Prentice Hall, 1964. | Zbl
,[10] The Interaction of Non-Linear Hyperbolic Waves, Comm. Pure Appl. Math., Vol. 41, 1988, pp. 569-590. | Zbl
,[11] Non-Linear Hyperbolic Differential Equations, Lectures notes, 1986- 1987, Lund University, Sweden, 1988, mineographied notes.
,[12] The Riemann Problem Near a Hyperbolic Singularity: the Classification of Solutions of Quadratic Riemann Problems I, S.I.A.M. J. Appl. Math., Vol. 48, 1988, pp. 1009-1032. | Zbl
, , and ,[13] The Classification of Solutions of Quadratic Riemann Problems II, S.I.A.M. J. Appl. Math., Vol. 48, 1988, pp. 1287-1301; III, S.I.A.M. J. Appl. Math., Vol. 48, 1988, pp. 1302-1318.
and ,[14] On the Cauchy Problem of a 2 × 2 Systems of Non-Strictly Hyperbolic Conservation Laws, Ph.D. Thesis, Courant Institute of Math. Sciences, N.Y. University, 1989.
,[15] A System of Non-Strictly Hyperbolic Conservation Laws Arising in Elasticity Theory, Arch. Rational Mech. Anal., Vol. 72, 1980, pp. 219- 241. | Zbl
and ,[16] First Order Quasi-Linear Equations with Several Space Variables, Mat. Sb., Vol. 123, 1970, pp. 228-255.
,[17] Asymptotic Solutions of Oscillatory Initial value Problems, Duke Math. J., Vol. 24, 1957, pp. 627-646. | Zbl
,[18] Shock Waves and Entropy, in Contributions to Nonlinear Functional Analysis, E. A. ZARANTONELLO Ed., Academic Press, 1971, pp. 603-634. | Zbl
,[19] Hyperbolic Systems of Conservation Laws and the Mathematical Theory of Shock Waves, S.I.A.M., Philadelphia, 1973. | Zbl
,[20] Zero Dissipative Limit for Conservation Laws, in Proceedings of the Conference on Non-linear Variational Problems and Partial Differential Equations, Isola d'Elba, 1990 (to appear).
,[21] The One-Dimensional Darcy's Law as the Limit of a Compressible Euler Flow, J. Differential Equations, 1990, pp. 129-147. | Zbl
and ,[22] Compacité par compensation, Ann. Scuola Norm. Sup. Pisa Cl. Sci., Vol. 5, 1978, pp. 489-507. | Numdam | Zbl
,[23] Partial Differential Equations, Iliffe Books, 1967. | Zbl
,[24] The Classification of 2 × 2 Systems of Non-Strictly Hyperbolic Conservation Laws, with Application to Oil Recovery, Comm. Pure Appl. Math., Vol. 40, 1987, pp. 141-178. | Zbl
and ,[25] Riemann Problems for Non-Strictly Hyperbolic 2 x 2 Systems of Conservation Laws, Trans. Amer. Math. Soc., Vol. 304, 1987, pp. 267- 306. | Zbl
and ,[26] La compacité par compensation pour les systèmes hyperboliques non linéaires de deux équations a une dimension d'espace, J. Math. Pures Appl., Vol. 65, 1986, pp. 423-468. | Zbl
,[27] Shock Waves and Reaction Diffusion Equations, Springer Verlag, 1983. | Zbl
,[28] Partial Differential Equations of Mathematical Physics, Pergamon Press, 1964. | Zbl
,[29] Compensated Compactness and Applications to Partial Differential Equations, in Nonlinear Analysis and Mechanics: Heriott-Watt Symposium, IV, Research Notes in Math., 1979, pp. 136-210. | Zbl
,[30] Global Existence of the Cauchy Problem for a Class of 2 x 2 Non-Strictly Hyperbolic Conservation Laws, Adv. in Appl. Math., Vol. 3, 1982, pp. 355-375. | Zbl
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