Uniqueness of a generalized entropy solution to the Cauchy problem for a quasilinear conservation law with convex flux-Reference-Cited by-同舟云学术

Uniqueness of a generalized entropy solution to the Cauchy problem for a quasilinear conservation law with convex flux

Published:2010-07-28 Issue:1 Volume:169 Page:98-112
ISSN:1072-3374
Container-title:Journal of Mathematical Sciences
language:en
Short-container-title:J Math Sci

Author:

Panov E. Yu.

Publisher

Springer Science and Business Media LLC

Subject

Applied Mathematics,General Mathematics,Statistics and Probability

Link

http://link.springer.com/content/pdf/10.1007/s10958-010-0041-8.pdf

Reference12 articles.

1. S. N. Kruzhkov, “First order quasilinear equations in several independent variables” [in Russian], Mat. Sb., 81, No. 2, 228–255 (1970); English transl.: Math. USSR Sb. 10, No. 2, 217–243 (1970).

2. A. Yu. Goritsky and E. Yu. Panov, “Example of nonuniqueness of entropy solution in the class of locally bounded functions,” Russian J. Math. Phys. 6, No. 4, 492–494 (1999).

3. A. Yu. Goritsky and E. Yu. Panov, “On locally bounded generalized entropy solutions of the Cauchy problem for a first-order quasilinear equation” [in Russian], Tr. Mat. Inst. Steklova 236, 120–133 (2002); English transl.: Proc. Steklov Inst. Math. 1, 110–123 (2002).

4. Ph. Bénilan, J. Carrillo, and P. Wittbold, “Renormalized entropy solutions of scalar conservation laws,” Ann. Sc. Norm. Super. Pisa, Cl. Sci. 29, 313–327 (2000).

5. E. Yu. Panov, “On the theory of generalized entropy solutions of the Cauchy problem for a first-order quasilinear equation in the class of locally integrable functions” [in Russian], Izv. Ross. Akad. Nauk Ser. Mat. 66, No. 6, 91–136 (2002); English transl.: Izv. Math. 66, No. 6, 1171–1218 (2002).