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.
Domains
Analysis of PDEs [math.AP]
Fichier principal
Gol_Tay_revised_2013_04_05.pdf (150.13 Ko)
Télécharger le fichier
Gol_Tay_corr_V2.pdf (140.31 Ko)
Télécharger le fichier
Origin : Files produced by the author(s)
Loading...