Global attractors for the extensible thermoelastic beam system

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:246

Article

Giorgi, C.¹  Naso, M. G.¹  Pata, V.²  Potomkin, M.³ 

[1] Univ Brescia, Dipartimento Matemat, I-25133 Brescia, Italy

[2] Politecn Milan, Dipartimento Matemat F Brioschi, I-20133 Milan, Italy

[3] Kharkov Natl Univ, Dept Math & Mech, UA-61077 Kharkov, Ukraine

关键词: Thermoelastic beam system;    Absorbing set;    Lyapunov functional;    Global attractor;    Backward uniqueness;    Rotational inertia;   

DOI  :  10.1016/j.jde.2009.02.020

来源: Elsevier

【 摘 要 】

This work is focused on the dissipative system [GRAPHICS] describing the dynamics of an extensible thermoelastic beam, where the dissipation is entirely contributed by the second equation ruling the evolution of theta. 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 P E R. The same result holds true when the first equation is replaced by partial derivative(u)u-gamma partial derivative(xxu)u + partial derivative(xxxx)u + partial derivative(xx)theta - (beta + parallel to partial derivative(x)u parallel to(2)(L2(0.1)))partial derivative(xx)u = f with gamma > 0. In both cases, the solutions on the attractor are strong solutions. (C) 2009 Elsevier Inc. All rights reserved.

【 授权许可】

Free