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On the Convergence to Equilibrium for Degenerate Transport Problems

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Abstract

We give a counterexample which shows that the asymptotic rate of convergence to the equilibrium state for the transport equation, with a degenerate cross section and in the periodic setting, cannot be better than t −1/2 in the general case. We suggest, moreover, that the geometrical properties of the cross section are the key feature of the problem and impose, through the distribution of the forward exit time, the speed of convergence to the stationary state.

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Authors and Affiliations

  1. Institut Géographique National, Laboratoire de Recherche en Géodésie, Paris, France

    Étienne Bernard

  2. Università degli Studi di Pavia, Pavia, Italy

    Francesco Salvarani

Authors
  1. Étienne Bernard
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  2. Francesco Salvarani
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Correspondence to Étienne Bernard.

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Communicated by L. Saint-Raymond

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Bernard, É., Salvarani, F. On the Convergence to Equilibrium for Degenerate Transport Problems. Arch Rational Mech Anal 208, 977–984 (2013). https://doi.org/10.1007/s00205-012-0608-2

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  • DOI: https://doi.org/10.1007/s00205-012-0608-2

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