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Relaxational trajectories: global approximations

Author

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  • Gorban, Alexander N.
  • Karlin, Iliya V.
  • Zmievskii, Vladimir B.
  • Nonnenmacher, T.F.

Abstract

The paper intends to fill the gap of analytic approximate methods for non-linear space-independent dissipative systems equipped with the entropy functional. The key point of the analysis is an upper limiting state in the beginning of the relaxation. Extremal properties of this state are described and explicit estimations are derived. This limiting state is used to construct explicit approximations of the phase trajectories. Special attention is paid to accomplish positivity, smoothness and the entropy growth along the approximate trajectories. The method is tested for the space-independent Boltzmann equation with various collisional mechanisms.

Suggested Citation

  • Gorban, Alexander N. & Karlin, Iliya V. & Zmievskii, Vladimir B. & Nonnenmacher, T.F., 1996. "Relaxational trajectories: global approximations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 231(4), pages 648-672.
    • Handle: RePEc:eee:phsmap:v:231:y:1996:i:4:p:648-672
    DOI: 10.1016/0378-4371(96)00090-8
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    Cited by:

    1. Gorban, Alexander N. & Karlin, Iliya V., 2004. "Uniqueness of thermodynamic projector and kinetic basis of molecular individualism," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 336(3), pages 391-432.
    2. Machado, Raúl, 2012. "On pressure and corner boundary conditions with two lattice Boltzmann construction approaches," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 84(C), pages 26-41.
    3. Gorban, Alexander N. & Karlin, Iliya V. & Zinovyev, Andrei Yu., 2004. "Invariant grids for reaction kinetics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 333(C), pages 106-154.

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