Exponential return to equilibrium for hypoelliptic quadratic systems

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• 作者：M. Ottobre^a ; ^{m.ottobre08@imperial.ac.uk} ; G.A. Pavliotis^a ; ^{g.pavliotis@imperial.ac.uk} ; K. Pravda-Starov^b ; ^{karel.pravda-starov@u-cergy.fr}
• 关键词：Quadratic operators ; Hypoellipticity ; Return to equilibrium ; Rate of convergence ; Chains of oscillators ; Generalized Langevin equation
• 刊名：Journal of Functional Analysis
• 出版年：2012
• 期刊代码：75_00221236
• 类别：mt
• 出版时间：1 May, 2012
• 卷：262
• 期：9
• 页码：4000-4039
• 文件大小：429 K

摘要

We study the problem of convergence to equilibrium for evolution equations associated to general quadratic operators. Quadratic operators are non-selfadjoint differential operators with complex-valued quadratic symbols. Under appropriate assumptions, a complete description of the spectrum of such operators is given and the exponential return to equilibrium with sharp estimates on the rate of convergence is proven. Some applications to the study of chains of oscillators and to the generalized Langevin equation are given.