Global smooth solutions of some quasi-linear hyperbolic systems with large data

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1. [1] Bouchut ( F.). - On zero pressure gas dynamics. Series on Advances in Mathematics for Applied Sciences, Kinetic Theory and Computing, B. Perthame edt, 22, 1994. Zbl0863.76068MR1323183
2. [2] Bouchut ( F.) and James ( F.). - Equations de transport unidimensionnelles à coefficients discontinus. C.R.A.S. Série 1, 320:1097-1102, 1995 and - One-dimensional transport equations with discontinuous coefficients. Nonlinear Anal. TMA, 32: 891-933, 1998. Zbl0989.35130
3. [3] Brenier ( Y.) and Grenier ( E.). - Sticky particles and scalar conservation laws. SIAM J. Numer. Anal., 35, no. 6:2317-2328, 1998. Zbl0924.35080MR1655848
4. [4] Diperna ( R.J.). - Compensated compactness and general systems of conservation laws. Trans. Amer. Math. Soc., 292:383-420, 1985. Zbl0606.35052MR808729
5. [5] Glimm ( J.). - Solutions in the large for nonlinear hyperbolic systems of equations. Com. Pure Appl. Math., 18:698-715, 1965. Zbl0141.28902MR194770
6. [6] Goudon ( T.) and Junca ( S.). - Vanishing pressure in gas dynamics equations. ZAMP, 51, no 1: 143-148, 2000. Zbl0970.35117MR1745295
7. [7] Grassin ( M.) and Serre ( D.). - Existence de solutions globales et régulières aux équations d'Euler pour un gaz parfait isentropique. C. R. Acad. Sci.Paris Sér. I Math., 325(7):721-726, 1997 and Grassin ( M.). - Global smooth solutions to Euler equation for a perfect gas. Indian Univ. Math. J., 47, no 4: 1397-1432, 1998. Zbl0887.35125MR1483706
8. [8] Grenier ( E.). - Existence globale pour le système des gaz sans pression. C.R.A.S. Série 1, 321:171-174, 1995. Zbl0837.35088MR1345441
9. [9] Hörmander ( L.). - Lectures on Nonlinear Hyperbolic Differential Equations,volume 26 of Mathématiques et Applications. Springer, 1997. Zbl0881.35001MR1466700
10. [10] Lax ( P.D.). - Hyperbolic systems of conservation laws and the mathematical theory of shock waves. In Regional Conf. in Appl. Math., volume 11, pages 1-48, Philadelphia, 1973. Zbl0268.35062MR350216
11. [11] Lions ( P.-L.). - Generalized solutions of Hamilton-Jacobi equations. Pitman, Boston, 1982. Zbl0497.35001MR667669
12. [12] Poupaud ( F.) and Rascle ( M.). - Measure solutions to the linear multi-dimensional transport equation with non-smooth coefficients. Comm. in PDE, 22:337-358, 1997. Zbl0882.35026MR1434148
13. [13] Serre ( D.). - Système de lois de conservation I et II. Diderot, Paris, New York, Amsterdam, 1996. Zbl0930.35002
14. [14] Zeldovich ( Ya B.). - Gravitational instability: an approximate theory for large density perturbations. Astron. Astrophys., 5:84, 1970.