Measure solutions to the linear multi-dimensional transport equation with non-smooth coefficients

Communications in Partial Differential Equations

Volumn 22, Issue 1-2, 1997, Pages 225-267

  Poupaud, F ^a   Rascle, M ^a  

^a CNRS   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000389658     PISSN: 03605302     EISSN: None     Source Type: Journal    
DOI: 10.1080/03605309708821265     Document Type: Article

References (19)

1. C. Bardos. Problèmes aux limites pour les équations aux dérivées partielles du premier ordre. Ann. Sci. Ecole norm. sup., 4:185-233, 1969.
2. F. Bouchut and F. James. Equations de transport unidimensionnelles à coefficients discontinus. C.R.A.S. Série 1, 320:1097-1102, 1995.
3. F. Bouchut and F. James. One-dimensional transport equation with discontinuous coefficients. Preprint, 1996.
4. Y. Brenier and E. Grenier. On the model of pressureless gases with sticky particles. CAM report, UCLA, 1994.
5. C. M. Dafermos. Generalized characteristics in hyperbolic systems of conservation laws. Arch. Rat. Mech. Anal., 107:127-155, 1989.
6. C.M. Dafermos. Characteristics in hyperbolic systems of conservation laws. In R.J. Knops, editor, Non-linear Analysis and Mechanics, volume 1, pages 1-58. Pitman, 1977.
7. Xiaxi Din and Caizhong Li. Some results on generalized solutions defined by Lebesgue-Stieltjes integral for hyperbolic conservation laws. In Sixth International Conference on Hyperbolic Problems, Hong-Kong, To appear 1996.
8. Xiaxi Ding. Theory of conservation laws in China. In J. Glimm, W. Graham anfd J.W. Grove, and B.J. Plohr, editors, Hyperbolic Problems : Theory, Numerics, Applications, pages 110-119. Stony Brook, World Scientific, 1994.
9. R.J. DiPerna and P.L. Lions. Ordinary differential equations, transport theory and Sobolev spaces. Invent. Math, 98 :511-547, 1989.
10. A. F. Filippov. Differential equation with discontinous right-hand side. Amer. Math. Soc. Transl., 42:199-231, 1962.
11. Ph. Le Floch. An existence and uniqueness result for two non strictly hyperbolic systems. Technical report, Centre de Mathématiques appliquées, Ecole Polytechnique, 1990.
12. V. Galkin. Functional solutions to conservation laws. Sov. Phys. Dokl., 35(2):133-135, 1990.
13. E. Grenier. Existence globale pour le système des gas sans pression. C.R.A.S. Série 1, 321:171-174, 1995.
14. J. Soler J.A. Carrillo. On functional kinetic equations of Vlasov type with bounded measures as initial data. Nonlinear Anal., to appear.
15. B. Keyfitz and H. Kranzer. A viscosity approximation to a system of conservation laws with no classical Riemann solution. In Nonlinear hyperbolic problems, volume 1042 of Lecture Notes in Math., New York, 1989.
16. D.J. Korchinski. Solution of a Riemann problem for a 2 × 2 system of conservation laws possessing no classical solution. PhD thesis, Adelphi university, 1977.
17. J. Rauch and M.C Read. Nonlinear superposition and absorption of delta-waves in one space dimension. J. Funct. Anal., 73:158-178, 1987.
18. D. Tan, T. Zhang, and Y. Zheng. Delta-shock waves as limits of vanishing viscosity method for hyperbolic systems of conservation laws. J. Diff. Eqns, 112:1-32, 1994.
19. A.I. Volpert. The space BV and quasi-linear equations,. Math USSR Sbornik, 2:225-267, 1967.