Viscous structure of singular shocks

Nonlinearity

Volumn 15, Issue 3, 2002, Pages 705-725

  Sever, Michael ^a  

^a HEBREW UNIVERSITY OF JERUSALEM   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0041471477     PISSN: 09517715     EISSN: None     Source Type: Journal    
DOI: 10.1088/0951-7715/15/3/311     Document Type: Article

References (20)

1. Cauret J J, Colombeau J F and Le Raux A Y 1989 Discontinuous generalized solutons of nonlinear nonconservative hyperbolic equations J. Math. Anal. Appl. 139 552-73
2. Dafermos C M and DiPerna R J 1976 The Riemann problem for certain classes of hyperbolic systems of conservation laws J. Diff. Eq. 20 90-114
3. Friedrichs K O and Lax P D 1971 Systems of conservation laws with a convex extension Proc. Nat. Acad. Sci USA 68 1686-8
4. Keyfitz B L and Kranzer H C 1995 Spaces of weighted measures for conservation laws with singular solutions J. Diff. Eq. 118 420-51
5. Keyfitz B L and Kranzer H C 1989 A viscous approximation to a system of conservation laws with no classical Riemann solution Nonlinear Hyperbolic Problems (Lecture Notes in Mathematics vol 1402) ed C Carasso (Berlin/New York: Springer) pp 185-97
6. Keyfitz B L and Kranzer H C 1990 A system of conservation laws with no classical Riemann solution Mathematics Department University Houston Preprint UH/MD86
7. Keyfitz B L 1999 Conservation laws, delta shocks and singular shocks Nonlinear Theory of Generalized Functions ed M Grosser, G Hermann, M Kunzinger and M Oberguggenberger (Boca Raton: Chapman and Hall/CRC press) pp 99-111
8. Klein D 1994 Existence of convex entropy densities for some strictly hyperbolic pairs of conservation laws PhD Thesis Mathematics Department, The Hebrew University of Jerusalem
9. Kranzer H C and Keyfitz B L 1990 A strictly hyperbolic system of conservation laws admitting singular shocks Nonlinear Evolution Equations that Change Type (IMA vol. Math. Appl. vol 27) ed B Keyfitz and M Shearer (Berlin/ New York: Springer) pp 107-25
10. Lax P D 1957 Hyperbolic systems of conservation laws, II Comm. Pure Appl. Math. 10 537-66
11. Mock M 1980 Systems of conservation laws of mixed type J. Diff. Eq. 37 70-88
12. Mock M 1980 A topological degree for orbits connecting critical points of autonomous systems J. Diff. Eq. 38 176-91
13. Rabinowitz P H 1986 Minimax methods in critical point theory with applications to differential equations AMS Regional Conference Series in Mathematics no 65
14. Rosenau P 1988 Evolution and breaking of ion-accoustic waves Phys. Fluids 31 1317-9
15. Schaeffer D G, Schecter S and Shearer M 1993 Nonstrictly hyperbolic conservation laws with a parabolic line J. Diff. Eq. 103 94-126
16. Sever M 2002 A class of nonlinear, nonhyperbolic systems of conservation laws with well-posed initial-value problems J. Diff. Eq. at press
17. Sever M 2001 Exchange of conserved quantities, shock loci and Riemann problems Math. Meth. Appl. Sci. 24 969-92
18. Li J and Zhang T 1997 Generalized Rankine-Hugoniot relations of delta-shocks in solution of transportation equations Proc. Int. Conf. PDE ed G Q Chen
19. Tan D, Zhang T and Zheng Y 1994 Delta-shock waves as limits of vanishing viscosity for hyperbolic system of conservation laws J. Diff. Eq. 112 1-32
20. Zheng Y 1998 Systems of conservation laws with incomplete sets of eigenvalues everywhere Advances in Nonlinear Partial Differential Equations and Related Areas ed Gui-Qiang Chen et al (Singapore: World Scientific)