학술논문
Global attractors for the extensible thermoelastic beam system
Document Type
Report
Author
Source
Journal of Differential Equations. May 1, 2009, Vol. 246 Issue 9, p3496, 22 p.
Subject
Language
English
ISSN
0022-0396
Abstract
To link to full-text access for this article, visit this link: http://dx.doi.org/10.1016/j.jde.2009.02.020 Byline: C. Giorgi (a), M.G. Naso (a), V. Pata (b), M. Potomkin (c) Keywords: 35B41; 37B25; 74F05; 74K10; 74H60 Abstract: This work is focused on the dissipative system {a.sub.ttu+a.sub.xxxxu+a.sub.xxI[cedilla]-([beta]+aa.sub.xu a.sub.L.sup.2(0,1).sup.2)a.sub.xxu=f,a.sub.tI[cedilla]-a.sub.xxI[cedilla]-a.sub.xxtu=g describing the dynamics of an extensible thermoelastic beam, where the dissipation is entirely contributed by the second equation ruling the evolution of I[cedilla]. Under natural boundary conditions, we prove the existence of bounded absorbing sets. When the external sources f and g are time-independent, the related semigroup of solutions is shown to possess the global attractor of optimal regularity for all parameters [beta][member of]R. The same result holds true when the first equation is replaced by a.sub.ttu-[gamma]a.sub.xxttu+a.sub.xxxxu+a.sub.xxI[cedilla]-([beta]+aa.sub.xu a.sub.L.sup.2(0,1).sup.2)a.sub.xxu=f with [gamma]0. In both cases, the solutions on the attractor are strong solutions. Author Affiliation: (a) Universita di Brescia, Dipartimento di Matematica, Via Valotti 9, 25133 Brescia, Italy (b) Politecnico di Milano, Dipartimento di Matematica "F. Brioschi", Via Bonardi 9, 20133 Milano, Italy (c) Kharkov National University, Department of Mathematics and Mechanics, 4 Svobody sq, 61077 Kharkov, Ukraine Article History: Received 29 May 2008; Revised 17 February 2009