On the Convergence to Equilibrium for Degenerate Transport Problems

Étienne Bernard; Francesco Salvarani

doi:10.1007/s00205-012-0608-2

On the Convergence to Equilibrium for Degenerate Transport Problems

Étienne Bernard
, Francesco Salvarani

IGN Institut Geographique National
University of Pavia

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

Résumé

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.

langue originale	Anglais
Pages (de - à)	977-984
Nombre de pages	8
journal	Archive for Rational Mechanics and Analysis
Volume	208
Numéro de publication	3
Les DOIs	https://doi.org/10.1007/s00205-012-0608-2
état	Publié - 1 juin 2013
Modification externe	Oui

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10.1007/s00205-012-0608-2

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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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AB - 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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On the Convergence to Equilibrium for Degenerate Transport Problems

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