Well posedness for pressureless flow

Communications in Mathematical Physics

Volumn 222, Issue 1, 2001, Pages 117-146

  Huang, Feimin ^a,b   Wang, Zhen ^c  

^a SISSA   (Italy)

^b INSTITUTE OF APPLIED MATHEMATICS   (China)

^c CITY UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035536273     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002200100506     Document Type: Article

References (24)

1. 1. Bouchut, F.: On zero pressure gas dynamics. Advances in kinetic theory and computing. Series on Advances in Mathematics for Applied Sciences, Vol. 22, Singapore: World Scientific, 1994, pp. 171-190
2. 2. Bouchut, F. and James, F.: One-dimensional transportation equations with discontinuous coefficients. Nonlinear Analysis TMA, 32, 891933 (1998)
3. 3. Bouchut, F. and James, F.: Duality solutions for pressureless gases, monotone scalar conservation laws and uniqueness. Comm. Part. Diff. Equs. 24, 2173-2190 (1999)
4. 4. Boudin, L.: A solution with bounded expansion rate to the model of viscous pressureless gases. SIAM J. Math. Anal. 32, No. 1, 172-193 (2000)
5. 5. Brenier, Y. and Grenier, E.: Sticky particles and scalar conservation laws. SIAM J. Num. Anal. 35 No.6, 2317-2328 (1998)
6. 6. Dafermos, C.: Generalized characteristics and the structure of solutions of hyperbolic conservation laws. Indiana Univ. Math. J. 26, No. 6, 1097-1119 (1977)
7. 7. Dal Maso, G., Le Floch, P. and Murat, F: Definition and weak stability of nonconservative products. J. Math. Pure Appl. 74, 483-548 (1995)
8. 8. Ding, X.: On a non-strictly hyperbolic system. Preprint, Dept. of Math., University of Jyvaskyla, No. 167 (1993)
9. 9. Ding, X. and Wang, Z.: Existence and Uniqueness of Discontinuous Solutions Defined by Lebesgue-Stieltjes Integral. Science in China (Series A) 39, No. 8, 807-819 (1996)
10. 10. E. W., Rykov, Y. and Sinai, Y: Generalized variational principles, global weak solutions and behavior with random initial data for systems of conservation laws arising in adhesion particle dynamics. Commun. Math. Phys. 177, 349-380 (1996)
11. xx. Comm. Pure Appl. Math. 3, 201-230 (1950)
12. 12. Hu, J.: The Riemann problem for pressureless fluid dynamics with distribution solutions in Colombeau's sense. Commun. Math. Phys. 194, 191-205 (1998)
13. 13. Huang, F. Li, C. and Wang, Z.: Solutions Containing Delta-Waves of Cauchy Problems for a Nonstrictly Hyperbolic System. Acta Math. Appl. Sinica, 4 (1995)
14. 14. Huang, F.: Existence and uniqueness of discontinuous solutions for a hyperbolic system. Proc. Roy. Soc. Edinb., Scotland, A 127, 1193-1205 (1997)
15. 15. Huang, F.: Existence and uniqueness of discontinuous solutions for a class of nonstrictly hyperbolic system. In: Advances in Nonlinear Partial Differential Equations and related areas, Singapore: Scientific Press, 1998, pp. 187-208
16. 16. Chen, S., Li, J. and Zhang, T: Explicit construction of measure solutions of the Cauchy problem for the transportation equations. Science in China (Series A), 40, 12, 1287-1299 (1997)
17. 17. Oleinik, O.: Discontinuous solutions of nonlinear differential equations. Am. Math. Soc. Transl. (2), 26, 95-172 (1963)
18. 18. Poupaud, F. and Rascle, M.: Measure solutions to the linear multidimensional transportation with discontinuous coefficients. Comm. Part. Diff. Equs. 22, 337-358 (1997)
19. 19. Sheng, W. and Zhang, T.: The Riemann problem for transportation equations in gas dynamics. Mem. Am. Math. Soc. 564, 137 (1999)
20. 20. Volpert, A.: The space BV and quasilinear equations. Mat. Sb. 73, 255-302 (1967); English translation in Math. USSR, Sb. 21, 225-267 (1967)
21. 20. Volpert, A.: The space BV and quasilinear equations. Mat. Sb. 73, 255-302 (1967); English translation in Math. USSR, Sb. 21, 225-267 (1967)
22. 21. Wang, Z., Huang, F. and Ding, X.: On the Cauchy problem of transportation equation. Acta Math. Appl. Sinica, 2, 113-122 (1997)
23. 22. Wang, Z. and Ding, X.: Uniqueness of generalized solution for the Cauchy problem of transportation equations. Acta Math. Scientia 17, 3, 341-352 (1997)
24. 23. Zeldovich, Y: Gravitational instability: An approximate theory for large density perturbations. Astron. & Astrophys. 5, 84-89 (1970)