Conservation laws, delta-shocks and singular shocks

Nonlinear Theory of Generalized Functions

Volumn , Issue , 2022, Pages 99-111

  Keyfitz, Barbara Lee ^a  

^a UNIVERSITY OF HOUSTON   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 85136470686     PISSN: None     EISSN: None     Source Type: Book    
DOI: None     Document Type: Chapter

References (20)

1. F. BOUCHUT: On zero pressure gas dynamics, in Advances in Kinetic Theory and Computing, Selected Papers, Volume 22 of Advances in Mathematics for Applied Sciences, pages 171-190, World Scientific 1994.
2. J. M. Burgers: A mathematical model illustrating the theory of turbulence, Advances in Applied Mathematics, 1:171-199, 1948.
3. J.-F. Colombeau: Multiplication of distributions, Bulletin of the American Mathematical Society, 23:251-268, 1990.
4. J. F. Colombeau and A. Y. Le Roux: Multiplications of distributions in elasticity and hydrodynamics, Journal of Mathematical Physics, 29:315-319, 1988.
5. J. K. Hunter and J. B. Keller: Weakly nonlinear high frequency waves, Communications on Pure and Applied Mathematics, XXXVL547-569, 1983.
6. B. L. Keyfitz and H. C. Kranzer: Existence and uniqueness of entropy solutions to the Riemann problem for hyperbolic systems of two nonlinear conservation laws, Journal of Differential Equations, 27:444-476, 1973.
7. B. L. Keyfitz and H. C. Kranzer: A system of hyperbolic conservation laws arising in elasticity theory, Archive for Rational Mechanics and Analysis, 72:219-241, 1980.
8. B. L. Keyfitz and H. C. Kranzer: The Riemann problem for a class of hyperbolic conservation laws exhibiting a parabolic degeneracy, Journal of Differential Equations, 47:35-65, 1983.
9. B. L. Keyfitz and H. C. Kranzer: A viscous approximation to a system of conservation laws with no classical Riemann solution, in C. Carasso et al., (eds), Nonlinear Hyperbolic Problems, pages 185-197. Springer, Lecture Notes in Mathematics 1402, Berlin 1989.
10. B. L. Keyfitz and H. C. Kranzer: Spaces of weighted measures for conservation laws with singular shock solutions, Journal of Differential Equations, 118:420-451, 1995.
11. D.J. Korchinski: Solution of a Riemann Problem for a 2 × 2 System of Conservation Laws Possessing No Classical Weak Solution, Ph.D. thesis, Adelphi University, Garden City, New York 1977.
12. P. Le Floch: Entropy weak solutions to nonlinear hyperbolic systems under nonconservative form, Communications in Partial Differential Equations, 13:669-727, 1988.
13. M. Oberguggenberger: Case study of a nonlinear, nonconservative, non-strictly hyperbolic system, Nonlinear Analysis, Theory, Methods and Applications, 19:53-79, 1992.
14. P. Rosenau: Evolution and breaking of ion-acoustic waves, Physics of Fluids, 31:1317-1319, 1988.
15. W. E, Y. G. Rykov, and Y. G. Sinai: Generalized variational principles, global weak solutions and behavior with random initial data for systems of conservation laws arising in adhesion particle dynamics, preprint.
16. D. G. Schaeffer, S. Schecter, and M. Shearer: Nonstrictly hyperbolic conservation laws with a parabolic line, Journal of Differential Equations, 103:94-126, 1993.
17. S. F. Shandarin and Y. B. Zeldovich: The large-scale structure of the universe: Turbulence, intermittency, structures in a self-gravitating medium, Reviews of Modern Physics, 61:185-220, 1989.
18. D. Tan, T. Zhang, and Y.-X. Zheng: Delta-shock waves as limits of vanishing viscosity for hyperbolic systems of conservation laws, Journal of Differential Equations, 112:1-32, 1994.
19. A. I. Vol pert: The spaces BV and quasilinear equations, Mathematics of the USSR Sbornik, 2(73):225-267, 1967.
20. Y. Zheng: Systems of conservation laws with incomplete sets of eigenvectors everywhere, in A Volume Dedicated to Professor Xiaqi Ding's 70th Birthday. to appear, 1998.