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Medientyp:
E-Artikel
Titel:
AN L²(Ω)-BASED ALGEBRAIC APPROACH TO BOUNDARY STABILIZATION FOR LINEAR PARABOLIC SYSTEMS
Beteiligte:
NAMBU, TAKAO
Erschienen:
Brown University, 2004
Erschienen in:Quarterly of Applied Mathematics
Sprache:
Englisch
ISSN:
0033-569X;
1552-4485
Entstehung:
Anmerkungen:
Beschreibung:
<p>We study the stabilization problem of linear parabolic boundary control systems. While the control system is described by a pair of standard linear differential operators (ℒ, τ), the corresponding semigroup generator generally admits no Riesz basis of eigenvectors. Very little information on the fractional powers of this generator is needed. In this sense our approach has enough generality as a prototype to be used for other types of parabolic systems. We propose in this paper a unified algebraic approach to the stabilization of a variety of parabolic boundary control systems. In the special case where the semigroup generator admits a Riesz basis, we also propose a new and simpler algebraic approach to the stabilization which is based on the so-called identity compensator. To show the usefulness of our approach, a class of linear boundary control systems of second order in t is introduced, to discuss the stabilization or the enhancement of stability of these systems.</p>