The continuous structure of discontinuities

II - Mathematical Analysis a - System of conservation laws
Part of the Lecture Notes in Physics book series (LNP, volume 344)


The regularization of discontinuities is discussed on the basis of molecular, computational and continuum considerations. Different regularization procedures may be implied by these distinct points of view. The mathematical motivation of regularization as an intermediate step in an existence proof is also of interest, but is not discussed in this paper.


Shock Wave Metastable State Detonation Wave Riemann Problem Wave Structure 
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  1. 1.
    Courant and Friedrichs, Supersonic Flow and Shock Waves, Springer-Verlag, New York, 1976.Google Scholar
  2. 2.
    W. Fickett and W. C. Davis, Detonation, Univ. of California Press, Berkeley, 1979.Google Scholar
  3. 3.
    B. Bukiet, “Applications of Front Tracking to Two Dimensional Curved Detonation Fronts,” SIAM J. Sci. Stat. Comp., vol. 9, pp. 80–99, 1988.Google Scholar
  4. 4.
    B. Bukiet, “The Effect of Curvature on Detonation Speed,” SIAM J. Appl. Math., To appear.Google Scholar
  5. 5.
    G. Caginalp, “An Analysis of a Phase Field Model of a Free Boundary,” Archive for Rational Mechanics and Analysis, vol. 92, pp. 205–245, 1986.Google Scholar
  6. 6.
    P. Colella, A. Majda, and V. Roytburd, “Theoretical and Numerical Structure for Reacting Shock Waves,” Siam J. Sci Stat Comp, vol. 7, pp. 1059–1080, 1986.Google Scholar
  7. 7.
    C. Gardner, J. Glimm, O. McBryan, R. Menikoff, D. H. Sharp, and Q. Zhang, “The Dynamics of Bubble Growth for Rayleigh-Taylor Unstable Interfaces,” Phys. of Fluids, In Press.Google Scholar
  8. 8.
    J. Glimm and X.L. Li, “On the Validation of the Sharp-Wheeler Bubble Merger Model from Experimental and Computational Data,” Phys. of Fluids, To appear.Google Scholar
  9. 9.
    J. Jones, “The Spherical Detonation,” Comm. Pure Appl. Math., To appear.Google Scholar
  10. 10.
    T.-P. Liu, “Hyperbolic Conservation Laws with Relaxation,” Comm. Math. Phys., vol. 108, pp. 153–175, 1987.Google Scholar
  11. 11.
    C. Mader, Numerical Modeling of Detonations, Univ. of California Press, Berkeley, 1979.Google Scholar
  12. 12.
    R. Menikoff and B. Plohr, “Riemann Problem for Fluid Flow of Real Materials,” Los Alamos preprint LA-UR-2259, 1987.Google Scholar
  13. 13.
    R. L. Rabie, G. R. Fowles, and W. Fickett, “The polymorphic Detonation” Physics of Fluids, vol. 22, pp. 422–435, 1979.Google Scholar
  14. 14.
    K. I. Read, “Experimental Investigation of Turbulent Mixing by Rayleigh-Taylor Instability,” Physica 12D, pp. 45–48, 1984.Google Scholar
  15. 15.
    D. H. Sharp, “Overview of Rayleigh-Taylor Instability,” Physica 12D, pp. 3–17, 1984.Google Scholar
  16. 16.
    M. Slemrod, “Admissibility Criteria for Propagating Phase Boundaries in a van der Waals Fluid,” Arch. Rat. Mech. Anal., vol. 81, pp. 303–319, 1983.Google Scholar
  17. 17.
    M. Slemrod, “Dynamic Phase Transitions in a Van Der Waals Fluid,” J Diff. Eq., vol. 52, pp. 1–23, 1984.Google Scholar
  18. 18.
    S. Stewart and J. B. Bdzil, “The Shock Dynamics of Stable Multidimensional Detonation,” J. Fluid Mech., To appear.Google Scholar
  19. 19.
    P. Thompson, G. Carofano, and Y.-G. Kim, “Shock Waves and Phase Changes in a Large Heat Capacity Fluid Emerging from a Tube,” J. Fluid Mech., vol. 166, pp. 57–92, 1986.Google Scholar
  20. 20.
    Forman Williams, Combustion Theory, Addison-Wesley Co., Reading, 1965.Google Scholar

Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  1. 1.Courant Institute of Mathematical SciencesNew York UniversityNew York

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