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Approach to Equilibrium of a Body Colliding Specularly and Diffusely with a Sea of Particles

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Abstract

We consider a rigid body acted upon by two forces, a constant force and the collective force of interaction with a continuum of particles. We assume that some of the particles that collide with the body reflect elastically (specularly), while others reflect probabilistically with some probability distribution K. We find that the rate of approach of the body to equilibrium is O(t −3−p) in three dimensions where p can take any value in (0, 2], depending on K.

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Authors and Affiliations

  1. Department of Mathematics, Brown University, Providence, RI, 02912, USA

    Xuwen Chen

  2. Department of Mathematics and Lefschetz Center for Dynamical Systems, Brown University, Providence, RI, 02912, USA

    Walter Strauss

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  1. Xuwen Chen
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  2. Walter Strauss
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Correspondence to Walter Strauss.

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Communicated by T.-P. Liu

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Chen, X., Strauss, W. Approach to Equilibrium of a Body Colliding Specularly and Diffusely with a Sea of Particles. Arch Rational Mech Anal 211, 879–910 (2014). https://doi.org/10.1007/s00205-013-0675-z

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  • DOI: https://doi.org/10.1007/s00205-013-0675-z

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