Nonhomogeneous dirichlet problems for degenerate parabolic-hyperbolic equations

Archive for Rational Mechanics and Analysis

Volumn 163, Issue 2, 2002, Pages 87-124

  Mascia, Corrado ^a   Porretta, Alessio ^b   Terracina, Andrea ^a  

^a SAPIENZA UNIVERSITY OF ROME   (Italy)

^b UNIVERSITY OF ROME TOR VERGATA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0036627684     PISSN: 00039527     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002050200184     Document Type: Article

References (17)

1. G. ANZELLOTTI, Pairings between measures and functions and compensated compactness, Ann. Mat. Pura ed Appl. 135 (1983), 293-318.
2. C. BARDOS, A. Y., LE ROUX & J.-C. NÉDÉLEC, First order quasilinear equations with boundary conditions, Comm. Partial Differential Equations 4 (1979), 1017-1034.
3. x + v, C. R. Acad. Sci. Paris Sér. I Math. 299 (1984), 919-922.
4. R. BÜRGER & K.H. KARLSEN, A strongly degenerate convection-diffusion problem modeling centrifugation of flocculated suspensions, Preprint (1999).
5. R. BÜRGER, S. EVJE & K.H. KARLSEN, On strongly degenerate convection-diffusion problems modeling sedimentation-consolidation processes, J. Math. Anal. Appl. 247 (2000), 517-556.
6. J. CARRILLO, Entropy solutions for nonlinear degenerate problems, Arch. Rational Mech. Anal. 147 (1999), 269-361.
7. G.-Q. CHEN & H. FRID, Divergence-measure fields and hyperbolic conservation laws, Arch. Rational Mech. Anal. 147 (1999), 89-118.
8. F. DUBOIS & P. LE FLOCH, Boundary conditions for nonlinear hyperbolic systems of conservation laws, Journal Differential Equations 71 (1988), 93-122.
9. R. EYMARD, T. GALLOUËT & R. HERBIN, The finite volume method, Handbook for Numerical Analysis, PH. CIARLET & J. L. LIONS eds, North Holland, Paris, 2000, 715-1022.
10. G. GAGNEUX & M. MADAUNE-TORT, Analyse mathématique de modeles nonlinéaires de l'ingégnerie pétroliere, Mathematiques & Applications, 22, Springer-Verlag, Berlin, 1996.
11. S.N. KRUŽKOV, First order quasilinear equations with several independent variables, (Russian) Mat. Sh. (N.S.) 81 (123), (1970), 228-255.
12. A. MICHEL & J. VOVELLE, A finite volume method for parabolic degenerate problems with general Dirichlet boundary conditions. In preparation.
13. J. MALEK, J. NECAS, M. ROKYTA & M. RUZICKA, Weak and measure-valued solutions to evolutionary PDEs, Applied mathematics and mathematical computation 13, London, Chapman & Hall, 1996.
14. F. OTTO, Initial-boundary value problem for a scalar conservation law, C. R. Acad. Sci. Paris Sér. I Math. 322 (1996), 729-734.
15. A. SZEPESSY, Measure-valued solutions of scalar conservation laws with boundary conditions, Arch. Rational Mech. Anal. 107 (1989), 181-193.
16. A. TERRACINA, Comparison properties for scalar conservation laws with boundary conditions, Nonlinear Anal. 28 (1997), 633-653.
17. J. VOVELLE, Convergence of finite volume monotone schemes for scalar conservation laws on bounded domains. Numer. Math. 90 (2002), 563-596.