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Boltzmann-Type Equation in Anelastic Case: A Convergence Result

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Abstract

In this Letter, a convergence result for the BBGKY hierarchy to a Boltzmann-like equation, in the case of an Anelastic collision, is shown. Boltzmann-like equations are often used to model dissipative dynamical systems such as granular media. This convergence result aims to make a contribution towards a mathematical foundation to these applications.

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References

  1. Lanford, O. III: Time evolution of large classical system, In: E. J. Moser (ed.), Lecture Notes in Phys. 38, Springer, New York, 1975, pp. 70–111.

    Google Scholar 

  2. Cercignani, C., Illner, R. and Pulvirenti, M.: The Mathematical Theory of Dilute Gases, Springer, New York, 1994.

    Google Scholar 

  3. Esipov, S. E. and Poschel, T.: The granular phase diagram, J. Stat. Physics, 1996.

  4. Brilliantov, N. V., Spahn, F. and Poschel, T.: A model for collision in granular gases, Zuberlin Humboldt Universitat.

  5. Benedetto, D., Caglioti, E. and Pulvirenti, M.: A kinetic equation for granular media, Math. Model. Numer. Anal. 31(5) (1997).

  6. Benedetto, D. and Caglioti, E.: The collapse phenomenon in one-dimensional inelastic point particle system, Physica D 132 (1999), 457–475.

    Google Scholar 

  7. Benedetto, D., Caglioti, E. and Pulvirenti, M.: A one dimensional Boltzmann equation with inelastic collisions, Rend. Sem. Mat. Fis. Milano (1999).

  8. Constantin, P., Grossman, E. and Mungan, M.: Inelastic collisions of three particles on a line as a two dimensional biliard, Physica D 83 (1995), 409–420.

    Google Scholar 

  9. Marchioro, C., Pellegrinotti, A., Presutti, E. and Pulvirenti, M.: On the dynamics of particles in a bounded region: A measure theoretical approach, J. Math. Phys. 17 (1976), 647–652.

    Google Scholar 

  10. Uchiyama, K.: On the Boltzmann–Grad limit for the Broadwell model of the Boltzmann equation, J. Statist. Phys. 52 (1988).

  11. Benedetto, D., Caglioti, E., Carrillo, J. A. and Pulvirenti, M.: A non Maxwellian steady distribution for one-dimensional granular media, J. Statist. Phys. 91 (1998), 979–990.

    Google Scholar 

  12. Bellomo, N., Esteban, M. and Lachowicz, M.: Nonlinear kinetic equation with dissipative collisions, Appl. Math. Lett. 8(5) (1995), 47–52.

    Google Scholar 

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Grilli, L. Boltzmann-Type Equation in Anelastic Case: A Convergence Result. Letters in Mathematical Physics 64, 119–127 (2003). https://doi.org/10.1023/A:1025716119825

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  • DOI: https://doi.org/10.1023/A:1025716119825

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