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Asymptotic Stability of Equilibrium States for Carleman and Godunov-Sultangazin Systems of Equations

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Abstract

One-dimensional systems of Carleman and Godunov-Sultangazin are studied for two and three groups of particles, respectively. These systems are a special case of the discrete Boltzmann kinetic equation. Theorems on existence of global solution to these systems for perturbations in the weighted Sobolev space are presented. Thus, an exponential stabilization to the equilibrium state is obtained.

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References

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Acknowledgments

The author is grateful to V. V. Palin and E. V. Radkevich for useful remarks and valuable discussions.

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Authors and Affiliations

  1. Department of Applied Mathematics, Moscow State University of Civil Engineering (MGSU), 26, Yaroslavskoye Shosse, Moscow, 129337, Russia

    S. A. Dukhnovskii

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  1. S. A. Dukhnovskii
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Correspondence to S. A. Dukhnovskii.

Additional information

Russian Text © The Author(s), 2019, published in Vestnik Moskovskogo Universiteta, Matematika. Mekhanika, 2019, Vol. 74, No. 6, pp. 55–57.

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Dukhnovskii, S.A. Asymptotic Stability of Equilibrium States for Carleman and Godunov-Sultangazin Systems of Equations. Moscow Univ. Math. Bull. 74, 246–248 (2019). https://doi.org/10.3103/S0027132219060068

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  • DOI: https://doi.org/10.3103/S0027132219060068

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