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The generalized Riemann problem for first order quasilinear hyperbolic systems of conservation laws I

Xiaosen Han|Shouxin Chen|Decheng Huang
대한수학회 (The Korean Mathematical Society)|2009.05|대한수학회보 (Bulletin of the KMS)|제46권 제3호|pp. 409-434

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참고문헌

키워드

quasilinear hyperbolic systemsgeneralized Riemann problemlocal solution
주제분류수학

초록

In this paper, we consider a generalized Riemann problem of the first order hyperbolic conservation laws. For the case that excludes the centered wave, we prove that the generalized Riemann problem admits a unique piecewise smooth solution u=u(t,x), and this solution has a structure similar to the similarity solution u=U(x/t) of the corresponding Riemann problem in the neighborhood of the origin provided that the coefficients of the system and the initial conditions are sufficiently smooth.

Abstract

In this paper, we consider a generalized Riemann problem of the first order hyperbolic conservation laws. For the case that excludes the centered wave, we prove that the generalized Riemann problem admits a unique piecewise smooth solution u=u(t,x), and this solution has a structure similar to the similarity solution u=U(x/t) of the corresponding Riemann problem in the neighborhood of the origin provided that the coefficients of the system and the initial conditions are sufficiently smooth.

참고문헌 (21)

  1. C. Gu, "A boundary value problem for hyperbolic systems and its applications", Acta Math. Sinica, 13, pp.32~48 (1963)
  2. The Cauchy problem of typical hyperbolic systems with discontinuous initial values, "C. Gu", Collections of Mathematical Papers of Fudan University, 1~16 (1960)
  3. The Cauchy problem of hyperbolic systems with discontinuous initial values, "C. Gu", Collections of Scientific and Technological Papers, 55~65 (1960)
  4. C. Gu, "Discontinuous initial value problems for systems of quasi-linear hyperbolic equations. I", Acta Math. Sinica, 11, pp.314~323
  5. C. Gu, "Discontinuous initial value problems for systems of quasi-linear hyperbolic equations. II", Acta Math. Sinica, 11, pp.324~327 (1961)
  6. C. Gu, "Discontinuous initial value problems for systems of quasi-linear hyperbolic equations. III", Acta Math. Sinica, 12, pp.132~143 (1962)
  7. C. M. Dafermos, "Hyperbolic Conservation Laws in Continuum Physics" (2000), Springer-Verlag
  8. P. D. Lax, "Hyperbolic systems of conservation laws. II", Comm. Pure Appl. Math, 10, pp.537~566 (1957)
  9. T. Li, "The generalized Riemann problem for quasilinear hyperbolic systems of conservation laws, Partial differential equations in China", Math. Appl., 288, pp.80~103 (1994), Kluwer Acad. Publ
  10. T. Li, "Local solvability of the boundary value problems for quasilinear hyperbolic systems", Sci. Sinica, 23(11), pp.1357~1367 (1980)
  11. T. Li, "Boundary value problems for the first-order quasilinear hyperbolic systems and their applications", J. Differential Equations, 41(1), pp.1~26 (1981)
  12. T. Li, "Probl`emes d onde centr´ee pourlas syst`emes hyperboliques quasilin´eaires et applications", C. R. Acad. Sci. Paris Ser. I Math, 299(9), pp.375~378 (1984)
  13. T. Li, "The discontinuous relations for quasilinear hyperbolic systems", Journal of Engineering Mathematics, 2(2), pp.1~10 (1985)
  14. T. Li, "The centered waves for quasilinear hyperbolic systems", Fudan Journal (Natural Science), 25, pp.195~206 (1986)
  15. T. Li, "The centered wave problem for quasilinear hyperbolic systems", Chin. Ann. Math., 7A, pp.423~436 (1986)
  16. T. Li, "A class of mixed problem for quasilinear hyperbolic systems with the initial axis being characteristic", Fudan Journal (Natural Science), 26, pp.1~9 (1987)
  17. T. Li, "The problem for quasilinear hyperbolic systems with discontinuous initial values", Journal of Engineering Mathematics, 4(2), pp.1~12 (1987)
  18. T. Li, "Boundary Value Problems for Quasilinear Hyperbolic Systems, Duke University Mathematics Series, V", Duke University, Mathematics Department, ~ (1985)
  19. J. Smoller, "Shock Waves and Reaction-Diffusion Equations" (1994), Springer-Verlag
  20. A. N. Tikhonov, "On discontinuous solutions of a quasilinear equation of first order", Dokl. Akad. Nauk SSSR (N.S.), 99, pp.27~30 (1954)
  21. J. Yu, "The regularity of solution for first order quasilinear hyperbolic systems", Chin. Ann. Math, 6A, pp.595~610 (1985)

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