Solutions in the large for certain nonlinear parabolic equations and applications

Royal Society of Edinburgh - Proceedings A

Volumn 126, Issue 1, 1996, Pages 19-45

  Zhao, Huijiang ^a   Zhu, Changjiang ^a  

^a INSTITUTE OF GEOLOGY AND GEOPHYSICS   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 21344440114     PISSN: 03082105     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0308210500030584     Document Type: Article

References (20)

1. G. Q. Chen. Limit behavior of approximate solutions to conservation laws. In Multidimensional hyperbolic problems and computations, IMA Vol. Math. Appl. 29, 38-57 (New York: Springer, 1991).
2. K. Chueh, C. Conley and J. Smoller. Positively invariant regions for systems of nonlinear diffusion equations. Indiana Univ. Math. J., 26 (1977), 373-92.
3. X. X. Ding and J. H. Wang. Global solutions for a semilinear parabolic system. Acta Math. Sci. 3 (1983), 397-414.
4. R. J. DiPerna. Convergence of approximate solutions to conservation laws. Arch. Rational Mech. Anal. 88 (1983), 23-70.
5. W. E. Fitzgibbon. Global existence for a particular convection diffusion system. In Lecture Notes in Mathematics 1285, eds I. W. Knowles and Y. Saito, 119-25 (Berlin: Springer, 1986).
6. A. Haraux. Nonlinear evolution equations - global behavior of solutions, Lecture Notes in Mathematics 841 (Berlin: Springer, 1981).
7. D. Hoff and J. Smoller. Solutions in the large for certain nonlinear parabolic systems. Anal. Non lineaire 2 (1985), 213-35.
8. P. T. Kan. On the Cauchy problem of a 2*2 system of nonstrictly hyperbolic conservation laws (Ph.D. thesis, Courtant Institute of Mathematical Science, 1989).
9. O. A. Ladyzenskaya, V. A. Solonnikov and N. N. Uraltseva. Linear and quasilinear equations of parabolic type, Amer. Math. Transl. (Providence, R.I.: American Mathematical Society, 1968).
10. P. D. Lax. Shock waves and entropy. In Contributions to Nonlinear Functional Analysis, ed. E. Zarantonello, 603-34 (New York: Academic Press, 1971).
11. Li Ta-tsien. Gl;obal regularity and the formation of singularity of solutions to first order quasilinear hyperbolic systems. Proc. Roy. Soc. Edinburgh Sect. A 87 (1981), 255-61.
12. Y. G. Lu. The global Holder-continuous solution of isentropic gas dynamics. Proc. Roy. Soc. Edinburgh Sect. A 123 (1993), 231-8.
13. Y. G. Lu. Global Holder continuous solutions of a nonstrictly hyperbolic system. J. Partial Differential Equations 17 (1994), 132-42.
14. Y. G. Lu and H. J. Zhao. Existence and asymptotic behaviors of solutions to 2*2 hyperbolic quadratic conservation laws with little viscosity. Nonlinear Anal. 17 (1991), 169-80.
15. Y. G. Lu, C. J. Zhu and H. J. Zhao. Properties of the viscous solutions to 2*2 hyperbolic quadratic conservation laws. Nonlinear Anal. 21 (1993), 485-99.
16. Y. G. Lu and C. J. Zhu. Existence and asymptotic behaviors of the viscous solutions to the inhomogeneous 2*2 hyperbolic quadratic conservation laws. J. Syst. Sci. Math. 13 (1993), 297-304.
17. F. Murat. Compactie par compensation: Condition necessaire et suffisante de continuité faible sous une hypothèse de rang constant. Ann. Scuola Norm. Sup. Pisa 8 (1981), 69-102.
18. D. Serre. Compacité par compensation et systèmes hyperboliques de lois de conservation. C. R. Acad. Sci. Paris, Ser. I 299 (1984), 555-8.
19. L. Tartar. The compensated compactness method applied to systems of conservation laws. In Systems of nonlinear PDE, ed. J. M. Ball, NATO ASI Series (New York: C. Reidel, 1983).
20. Zhu Changjiang, Li Caizhong and Zhao Huijiang. Existence of global continuous solutions to a class of nonstrictly hyperbolic conservation laws. Acta Mathematica Scientia 14 (1994), 96-106.