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

Research output: Contribution to journal › Article › peer-review

13 Citations (Scopus)

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.

Original language	English
Pages (from-to)	977-984
Number of pages	8
Journal	Archive for Rational Mechanics and Analysis
Volume	208
Issue number	3
DOIs	https://doi.org/10.1007/s00205-012-0608-2
Publication status	Published - 1 Jun 2013
Externally published	Yes

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title = "On the Convergence to Equilibrium for Degenerate Transport Problems",

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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AU - Salvarani, Francesco

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N2 - 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.

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.

UR - https://www.scopus.com/pages/publications/84877077916

U2 - 10.1007/s00205-012-0608-2

DO - 10.1007/s00205-012-0608-2

M3 - Article

AN - SCOPUS:84877077916

SN - 0003-9527

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EP - 984

JO - Archive for Rational Mechanics and Analysis

JF - Archive for Rational Mechanics and Analysis

IS - 3

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On the Convergence to Equilibrium for Degenerate Transport Problems

Abstract

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