A new entropy functional for a scalar conservation law

Communications on Pure and Applied Mathematics

Volumn 52, Issue 11, 1999, Pages 1427-1442

  Liu, Tai Ping ^a   Yang, Tong ^b  

^a STANFORD UNIVERSITY   (United States)

^b CITY UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033470637     PISSN: 00103640     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1097-0312(199911)52:11<1427::AID-CPA2>3.0.CO;2-R     Document Type: Article

References (14)

1. Bressan, A.; Crasta, G.; Piccoli, B. Well posedness of the Cauchy problem for n × n systems of conservation laws. Mem. Amer. Math. Soc., to appear.
2. Kružkov, S. N. First order quasilinear equations with several independent variables. (Russian) Mat. Sb. (N. S.) 81 (123) (1970), 228-255. English transl. in Math. USSR Sb. 10 (1970), 217-273.
3. Kružkov, S. N. First order quasilinear equations with several independent variables. (Russian) Mat. Sb. (N. S.) 81 (123) (1970), 228-255. English transl. in Math. USSR Sb. 10 (1970), 217-273.
4. Lax, P. D. Hyperbolic systems of conservation laws. II. Comm. Pure Appl. Math. 10 (1957), 537-566.
5. Lax, P. D. Shock waves and entropy. Contributions to nonlinear functional analysis (Proc. Sympos., Math. Res. Center, Univ. Wisconsin, Madison, Wis., 1971), 603-634. Academic Press, New York, 1971.
6. Lax, P. D. Hyperbolic systems of conservation laws and the mathematical theory of shock waves. Conference Board of the Mathematical Sciences Regional Conference Series in Applied Mathematics, No. 11. Society for Industrial and Applied Mathematics, Philadelphia, 1973.
7. 1 stability for 2 × 2 systems of hyperbolic conservation laws. J. Amer. Math. Soc., to appear.
8. Liu, T.-P.; Yang, Y. Well-posedness theory for hyperbolic conservation laws. Comm. Pure Appl. Math. 52 (1999), no. 12, to appear.
9. 1 boundedness of solutions of hyperbolic conservation laws. Methods and Appl. Anal. 4 (1997), no. 3, 339-355.
10. 1-contractive semigroup, Comm. Pure Appl. Math. 24 (1971), 125-132.
11. Schaeffer, D. G. A regularity theorem for conservation laws. Advances in Math. 11 (1973), 368-386.
12. Smoller, J. Shock waves and reaction-diffusion equations. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Science], 258. Springer-Verlag, New York-Berlin, 1983.
13. Tartar, L. Compensated compactness and applications to partial differential equations. Nonlinear analysis and mechanics: Heriot-Watt Symposium, Vol. IV, 136-212. Res. Notes in Math., 39, Pitman, Boston-London, 1979.
14. Tartar, L. Compensated compactness and applications to partial differential equations. Nonlinear analysis and mechanics: Heriot-Watt Symposium, Vol. IV, 136-212. Res. Notes in Math., 39, Pitman, Boston-London, 1979.