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Thermoelasticity

  • Igor Chueshov
  • Irena Lasiecka
Chapter
Part of the Springer Monographs in Mathematics book series (SMM)

Abstract

In this chapter we undertake a study of asymptotic behavior of solutions associated with von Karman evolution equations subject to thermal dissipation. We consider models with and without the rotational inertia terms. The presence of this parameter changes the character of the thermoelastic dynamics from parabolic-like to hyperbolic-like. We establish the existence of a compact global attractor of finite fractal dimension and study its properties. Our main tool is the stabilizability estimate which asserts that a difference of any two trajectories can be exponentially stabilized to zero modulo compact perturbation. This estimate is independent of the value of rotational inertia parameter α and heat/thermal capacity κ. This makes it possible to obtain estimates for the dimension and size of the attractor which do not depend on the parameters α and κ. We also prove upper semicontinuity of the attractor with respect to the parameters α and κ. In the case κ → 0 we show that the attractor is close in some sense to the attractor of an isothermal structurally damped von Karman model. In this chapter we mainly follow [76].

Keywords

Fractal Dimension Lyapunov Function Unstable Manifold Global Attractor Rotational Inertia 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© Springer Science+Business Media 2010

Authors and Affiliations

  1. 1.Department of Mechanics & MathematicsKharkov National UniversityKharkovUkraine
  2. 2.Department of MathematicsUniversity of VirginiaCharlottesvilleUSA

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