# American Institute of Mathematical Sciences

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

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.
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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