Existence of solutions to hyperbolic conservation laws with a source

Communications in Mathematical Physics

Volumn 187, Issue 2, 1997, Pages 327-340

  Klingenberg, Christian ^a   Lu, Yun Guang ^b  

^a UNIVERSITY OF WÜRZBURG   (Germany)

^b INSTITUTE OF GEOLOGY AND GEOPHYSICS   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031476398     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002200050138     Document Type: Article

References (22)

1. Chen, G.Q.: Convergence of the Lax-Friedrichs scheme for isentropic gas dynamics. Acta Math. Sc. 1 (1986)
2. Chen, G.Q., Glimm, J.: Global solutions to the compressible Euler equations with geometric structure. Preprint SUNYSB-95, Stony Brook (1995), Commun. Math. Phys. 180 (1996)
3. Diperna, R.J.: Convergence of approximate solutions to conservation laws. Arch. Rat. Mech. Anal., 82 (1983)
4. Diperna, R.J.: Convergence of the viscosity method for isentropic gas dynamics. Commun. Math. Physics, 91 (1983)
5. Earnshaw, S.: On the mathematical theory of sound. Phil. Trans. 150 (1858)
6. Embid, P., Goodman, J., Majda, A.: Multiple steady steady states for 1-d transsonic flow. SIAM J. Sci. Stat. Comp. 5, 1 (1984)
7. Glimm, J., Marshall, G., Plohr, B.: A generalized Riemann Problem for quasi-one-dimensional gas flows. Adv. Appl. Math. 5 (1984)
8. Isaacson, E., Temple, B.: Nonlinear resonance in systems of conservation laws. SIAM J. Appl. Math. 52 (1992)
9. Kamke, E.: Differentialgleichungen, Lösungsmethoden und Lösungen: 1. Gewöhnliche Differential-gleichungen, sixth ed., Leipzig: Akademische Verlagsanstalt, 1959
10. Klingenberg, C., Lu, Y.: Existence of solutions to resonant systems of conservation laws. Preprint 94-28(SFB 359), Heidelberg University (1994)
11. Klingenberg, C., Lu, Y.: The vacuum case in Diperna's paper. Preprint SFB359, Heidelberg University (1996)
12. LeRoux, A.Y: Numerical stability for some equations of gas dynamics. Mathematics of Computation 37 (1981)
13. Lions, P.L., Perthame B., Sougandis, S.E.: Existence and stability of entropy solutions for the hyperbolic systems of isentropic gas dynamics in Eulerian and Lagrangian coordinates. Preprint (1995)
14. Lions, P.L., Perthame, B., Tadmor, : Kinetic formulation of the isentropic gas dynamics and p-system. Commun. Math. Phys. 163 (1994)
15. Liu, T.P.: Quasilinear hyperbolic systems. Commun. Math. Phys. 68 (1979)
16. Liu, T.P.: Resonance for a quasilinear hyperbolic equation. J. Math. Phys. 28 (1987)
17. Lu, Y.G.: Convergence of the viscosity method for a nonstrictly hyperbolic conservation law. Commun. Math. Phys. 150 (1992)
18. Lu, Y.G.: Hölder continuous solutions of isentropic gas dynamics. Proc. Royal Soc. Edinburgh, Vol. 123A (1993)
19. Lu, Y.G.: Convergence of the viscosity method for some nonlinear hyperbolic systems. Proc. Royal Soc. Edinburgh, Vol. 124A (1994)
20. Lu, Y.G.: An explicit bound of viscosity solutions to isentropic gas dynamics and Euler equations. University of Heidelberg preprint, Series SFB 359, 95-18 (1995)
21. Nagumo, M.: Proc. Phys.-math. Soc. Japan. 3, 21 (1937)
22. Whitham, G.B.: Linear and nonlinear waves. New York: John Wiley and Sons, (1973)