Rocky Mountain Journal of Mathematics

On a Quasilinear Degenerate Hyperbolic System of Conservation Laws Describing Nonlinear Advection Phenomena

Ling Hsiao and Piero De Mottoni

Full-text: Open access

Article information

Source
Rocky Mountain J. Math., Volume 21, Number 4 (1991), 1327-1369.

Dates
First available in Project Euclid: 5 June 2007

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1181072910

Digital Object Identifier
doi:10.1216/rmjm/1181072910

Mathematical Reviews number (MathSciNet)
MR1147863

Zentralblatt MATH identifier
0802.35096

Citation

Hsiao, Ling; Mottoni, Piero De. On a Quasilinear Degenerate Hyperbolic System of Conservation Laws Describing Nonlinear Advection Phenomena. Rocky Mountain J. Math. 21 (1991), no. 4, 1327--1369. doi:10.1216/rmjm/1181072910. https://projecteuclid.org/euclid.rmjm/1181072910


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References

  • R. Aris and N. Amundson, Mathematical methods in chemical engineering, Vol. 2, Prentice-Hall Inc., Englewood Cliffs, NJ 1973.
  • C.M. Dafermos and L. Hsiao, Hyperbolic systems of balance laws with inhomogeneity and dissipation, Indiana Univ. Math. J. 31 (1982), 471-491.
  • J. Glimm, Solutions in the large for nonlinear hyperbolic systems of equations, Comm. Pure Appl. Math. 18 (1965), 697-715.
  • L. Hsiao and T. Chang, Perturbation of the Riemann problem in gas dynamics, J. Math. Anal. Appl. 79 (1981), 436-460.
  • F. Helferich and G. Klein, Multicomponent chromatography, Marcel Dekker Inc., New York, 1970.
  • E. Isaacson, Global solutions of Riemann problems for a non-strictly hyperbolic system of conservation laws arising in enhanced oil recovery, J. Comp. Phys., to appear.
  • B. Keyfitz and H. Kranzer, A system of non-strictly hyperbolic conservation laws arising in elasticity theory, Arch. Rat. Mech. Anal. 72 (1980).
  • P.D. Lax, Hyperbolic systems of conservation laws II, Comm. Pure Appl. Math. 10 (1957), 537-566.
  • --------, Shock waves and entropy, in Contributions to nonlinear functional analysis (E. Zarantonello, Ed.), Academic Press, New York, 1971, 603-634.
  • T.-P. Liu, Approximation and qualitative behavior of admissible solutions of hyperbolic conservation laws, Mem. Amer. Math. Soc. (1984).
  • -------- and C.H. Wang, On a hyperbolic system of conservation laws which is not strictly hyperbolic, MRC Technical Summary Report No. 2184, Dec. 1980.
  • J.D. Murray and J.E.R. Cohen, On nonlinear convective dispersal effects in an interacting population model, SIAM J. Appl. Math., 43 (1983), 66-78.
  • H. Rhee, R. Aris and N.R. Amundson, On the theory of multicomponent chromatography, Phil. Trans. Roy. Soc. A267 (1970), London, 419-.
  • B. Temple, Global solutions of the Cauchy problem for a class of $2\times2$ non strictly hyperbolic conservation laws, Adv. in Appl. Math. 3 (1982), 335-375.