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| Regular Global Attractors of Type III Thermoelastic Extensible Beams |
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Citation： |
Michele COTI ZELATI,Vittorino PATA,Ramon QUINTANILLA.Regular Global Attractors of Type III Thermoelastic Extensible Beams[J].Chinese Annals of Mathematics B,2010,31(5):619~630 |
| Page view： 1790
Net amount： 1272 |
Authors： |
Michele COTI ZELATI; Vittorino PATA; Ramon QUINTANILLA; |
Foundation： |
the Spanish Ministry of Science and Technology through the Project “Partial
Defferential Equations in Thermomechanics. Theory and Applications” (No. MTM2009-08150). |
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| Abstract： |
For $\beta \in \R$, the authors consider the evolution system in the
unknown variables $u$ and $\alpha$
$$
\left\{\!\!\! \begin{array}{l}
\ds \ptt u+\partial_{xxxx}u+\partial_{xxt}\alpha-(\beta+\|\partial_x u\|^2_{L^2})\partial_{xx}u=f, \\ds \ptt \alpha - \partial_{xx} \alpha-\partial_{xxt}
\alpha-\partial_{xxt}u=0
\end{array} \right.
$$
describing the dynamics of type III thermoelastic extensible beams,
where the dissipation is entirely contributed by the second equation
ruling the evolution of the thermal displacement $\alpha$. Under
natural boundary conditions, the existence of the global attractor
of optimal regularity for the related dynamical system acting on the
phase space of weak energy solutions is established. |
Keywords： |
Type III thermoelastic extensible beam, Lyapunov functional, Global
attractor |
Classification： |
35B41, 37B25, 74F05, 74K10 |
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