Hyperbolic regularizations of conservation laws View Full Text


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Article Info

DATE

2008-09

AUTHORS

V. V. Palin, E. V. Radkevich

ABSTRACT

One of the problems of the kinetics of nonequilibrium processes is related to the lack of information concerning most of the nonequilibrium variables, namely, those which have no intuitive physical meaning, i.e., cannot be defined from the experiment. Moreover, the number of nonequilibrium variables is so large that a reasonable amount (from the physical point of view) of boundary conditions is insufficient for posing the mixed problem. What do the initial data for the Cauchy problem and the boundary conditions for the mixed problem mean in this case? In fact, we must assume that the initial-boundary data for most of the nonequilibrium variables (the higher-order momenta) are arbitrary! The British physicists Chapman and Enskog conjectured that, for “physically correct” models of continuum mechanics, the influence of the higher-order momenta is “inessential.” There are some postulates of physical correctness, but we do not dwell on them. For us it is of importance to understand what the fact that the influence of the higher-order momenta is “inessential” means from the mathematical point of view. The paper is devoted to this very topic. More... »

PAGES

343-363

References to SciGraph publications

  • 2005-10. Restrictions of Quadratic Forms to Lagrangian Planes, Quadratic Matrix Equations, and Gyroscopic Stabilization in FUNCTIONAL ANALYSIS AND ITS APPLICATIONS
  • 2000-04. Temperature jump and velocity slip in the moment method in CONTINUUM MECHANICS AND THERMODYNAMICS
  • 1993. Extended Thermodynamics in NONE
  • 1993-03. Heat pulse experiments revisited in CONTINUUM MECHANICS AND THERMODYNAMICS
  • 2008. Irreducible Chapman–Enskog Projections and Navier–Stokes Approximations in INSTABILITY IN MODELS CONNECTED WITH FLUID FLOWS II
  • 1996-06. Moment closure hierarchies for kinetic theories in JOURNAL OF STATISTICAL PHYSICS
  • 2005. Invariant Manifolds for Physical and Chemical Kinetics in NONE
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    http://scigraph.springernature.com/pub.10.1134/s1061920808030051

    DOI

    http://dx.doi.org/10.1134/s1061920808030051

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    https://app.dimensions.ai/details/publication/pub.1025130911


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