A compactness result for perturbed semigroups and application to a transport model

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:359

Article

Latrach, K.¹  Megdiche, H.²  Taoudi, M. A.² 

[1] Univ Clermont Ferrand, Math Lab, CNRS, UMR 66220, F-63177 Aubiere, France

[2] Fac Sci Gabes, Dept Math, Zrig, Gabes, Tunisia

关键词: Strongly continuous semigroups;    Dyson-Phillips expansion;    Transport operator;    Reflecting boundary conditions;   

DOI  :  10.1016/j.jmaa.2009.05.027

来源: Elsevier

【 摘 要 】

In this paper we are concerned with the compactness properties of remainder terms of the Dyson-Phillips expansion of perturbed semigroups on general Banach spaces. More specifically, we derive conditions which ensure the compactness of the remainder term R(n)(t) for some integer n. Our result applies directly to discuss the time asymptotic behaviour (for large times) of the solution of a one-dimensional transport equation with reentry boundary conditions on L(1)-spaces without regularity conditions on the initial data. (C) 2009 Elsevier Inc. All rights reserved.

【 授权许可】

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