L1 stability for systems of conservation laws with a nonresonant moving source

SIAM Journal on Mathematical Analysis

Volumn 33, Issue 2, 2001, Pages 411-439

  Ha, Seung Yeal ^a  

^a STANFORD UNIVERSITY   (United States)

Author keywords

Conservation laws; L1 stability; Nonlinear functional

Indexed keywords

EID: 0036045705     PISSN: 00361410     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036141000373045     Document Type: Article

References (30)

1. D. AMADORI AND G. GUERRA, Uniqueness and continuous dependence for systems of balanced laws with dissipation, Nonlinear Anal., submitted.
2. A. BRESSAN, A locally contractive metrics for systems of conservation laws, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 22 (1995), pp. 109-135.
3. A. BRESSAN AND R. M. COLOMBO, The semigroup generated by 2 × 2 conservation laws, Arch. Ration. Mech. Anal., 133 (1995), pp. 1-75.
4. A. BRESSAN, G. CRASTA, AND B. PICCOLI, Well Posedness of the Cauchy Problem for n × n Systems of Conservation Laws, Mem. Amer. Math. Soc., 146 (2000).
5. A. BRESSAN AND P. LEFLOCH, Uniqueness of weak solutions to systems of conservation laws, Arch. Ration. Mech. Anal., 140 (1997), pp. 301-317.
6. 1 stability estimates for n × n conservation laws, Arch. Ration. Mech. Anal., 149 (1999), pp. 1-22.
7. G. Q. CHEN AND J. GLIMM, Global solutions to the compressible Euler equations with geometrical structure, Comm. Math. Phys., 180 (1996), pp. 153-193.
8. R. COURANT AND K. O. FRIEDRICHS, Supersonic Flow and Shock Waves, Interscience, New York, 1948.
9. G. CRASTA AND B. PICCOLI, Viscosity solutions and uniqueness for systems of inhomogeneous balance laws, Discrete Contin. Dynam. Systems, 3 (1997), pp. 477-502.
10. J. GLIMM, Solutions in the large for nonlinear hyperbolic systems of equations, Comm. Pure Appl. Math., 18 (1965), pp. 697-715.
11. J. GLIMM AND P. D. LAX, Decay of Solutions of Systems of Hyperbolic Conservation Laws, Mem. Amer. Math. Soc. 101, AMS, Providence, RI, 1970.
12. A. L. HOFFMAN, A single fluid model for shock formation in MHD shock tubes, J. Plasma. Phys., 1 (1967), pp. 192-207.
13. 1-contractive semigroup, Comm. Pure Appl. Math., 24 (1971), pp. 125-132.
14. S. N. KRUSHKOV, Generalized solutions of the Cauchy problem in the large for nonlinear equations of first order, Dokl. Akad. Nauk, 187 (1969), pp. 29-32 (in Russian).
15. P. D. LAX, Hyperbolic systems of conservation laws II, Comm. Pure Appl. Math., 10 (1957), pp. 537-566.
16. P. D. LAX, Shock waves and entropy, in Contributions to Nonlinear Functional Analysis, E. Zarantonello, ed., Academic Press, New York, 1971, pp. 603-634.
17. W.-C. LIEN, Hyperbolic conservation laws with a moving source, Comm. Pure Appl. Math., 52 (1999), pp. 1075-1098.
18. T.-P. LIU, The deterministic version of the Glimm scheme, Comm. Math. Phys., 57 (1975), pp. 135-148.
19. T.-P. LIU, Quasilinear hyperbolic systems, Comm. Math. Phys., 68 (1979), pp. 141-172.
20. T.-P. LIU, Nonlinear stability and instability of transonic gas flows through a nozzle, Comm. Math. Phys., 83 (1982), pp. 243-260.
21. T.-P. LIU, Nonlinear resonance for quasilinear hyperbolic equation, J. Math. Phys., 28 (1987), pp. 2593-2602.
22. T.-P. LIU AND T. YANG, A new entropy functional for a scalar conservation law, Comm. Pure Appl. Math., 52 (1999), pp. 1427-1442.
23. 1 stability for 1 × 2 systems of hyperbolic conservation laws, J. Amer. Math. Soc., 12 (1999), pp. 729-774.
24. T.-P. LIU AND T. YANG, Well posedness theory for hyperbolic conservation laws, Comm. Pure Appl. Math., 52 (1999), pp. 1553-1586.
25. O. A. OLEINIK, Discontinuous solutions of nonlinear differential equations, Uspekhi Mat. Nauk, 12 (1957), pp. 3-73 (in Russian);
26. Amer. Math. Soc. Transl. Ser. 2, 26 (1963), pp. 95-172 (in English).
27. J. SMOLLER, Shock Waves and Reaction-Diffusion Equations, Springer-Verlag, New York, 1982.
28. 1-contractive metrics for system of conservation laws, Trans. Amer. Math. Soc., 288 (1985), pp. 471-480.
29. A. VOLPERT, The space BV and quasilinear equations, Mat. Sb., 73 (1967), pp. 255-302 (in Russian);
30. Mat. USSR-Sb., 2 (1967), pp. 225-267 (in English).