On permanent regimes for non-autonomous linear evolution equations in Banach spaces with applications to transport theory

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September 2010, 3(3): 473-499. doi: 10.3934/krm.2010.3.473

On permanent regimes for non-autonomous linear evolution equations in Banach spaces with applications to transport theory

1.	Université de Franche–Comté, Laboratoire de Mathématiques, CNRS UMR 6623, 16, route de Gray, 25030 Besançon Cedex

Received September 2008 Revised February 2010 Published July 2010

Abstract
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This paper deals with existence and uniqueness of permanent (i.e. defined for all time $t\in \mathbb{R}$) solutions of non-autonomous linear evolution equations governed by strongly stable (at $-\infty $) evolution families in Banach spaces and driven by permanent bounded forcing terms. In particular, we study the existence and uniqueness of (asymptotically) almost-periodic solutions driven by (asymptotically) almost-periodic forcing terms. Systematic applications to some non-autonomous linear kinetic equations in arbitrary geometries relying on their dispersive properties are given.

Keywords: non-autonomous linear equations in Banach spaces, almost-periodic solutions, kinetic equations, periodic solutions, dispersive properties..

Mathematics Subject Classification: 47D06, 35F10, 35B1.

Citation: Mustapha Mokhtar-Kharroubi. On permanent regimes for non-autonomous linear evolution equations in Banach spaces with applications to transport theory. Kinetic & Related Models, 2010, 3 (3) : 473-499. doi: 10.3934/krm.2010.3.473

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