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Journal Articles Journal of Statistical Physics Year : 2013

Optimal estimate of the spectral gap for the degenerate Goldstein-Taylor model

Abstract

In this paper we study the decay to the equilibrium state for the solution of a generalized version of the Goldstein-Taylor system, posed in the one-dimensional torus $\T=\R/\Z$, by allowing that the non-negative cross section $\sigma$ can vanish in a subregion $X:=\{ x \in \T\, \vert \, \sigma(x)=0\}$ of the domain with $\text{meas}\,(X)\geq 0$ with respect to the Lebesgue measure. We prove that the solution converges in time, with espect to the strong $L^2$-topology, to its unique equilibrium with an exponential rate whenever $\text{meas}\,(\T \setminus X)\geq 0$ and we give an optimal estimate of the spectral gap.
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Dates and versions

hal-00766211 , version 1 (18-12-2012)
hal-00766211 , version 2 (03-05-2013)

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Etienne Bernard, Francesco Salvarani. Optimal estimate of the spectral gap for the degenerate Goldstein-Taylor model. Journal of Statistical Physics, 2013, 153 (2), pp.363-375. ⟨10.1007/s10955-013-0825-6⟩. ⟨hal-00766211v2⟩

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