Global Attractors for an Extensible Thermoelastic Beam System

This work is focused on the dissipative system describing the dynamics of an extensible thermoelastic beam, where the dissipation is entirely contributed by the second equation ruling the evolution of the temperature. Under natural boundary conditions, we prove the existence of bounded absorbing sets. When both the external body force and the heat source are time-independent, the related semigroup of solutions is shown to possess the global attractor of optimal regularity for all values of the external axial load. The same result holds true when the rotational inertia is taken into consideration. In both cases, the solutions on the attractor are strong solutions.Comment: 21 pages, no figur

Extension of the controllability concept from the finite dimension to the infinite dimension: exact, approximate, null controllability

Mémoire du D.E.A. Mathématiques et Applications, UFR des Sciences et des Thechniques, Université de Franche-Comté, Besançon, France

Modélisation, contrôle, stabilité et approximation numérique des modèles thermo- et (ou) visco-élastiques

Thèse n. 967, UFR des Sciences et des Thechniques, Université de Franche-Comté, Besançon, Franc

Exponential stability in linear heat conduction with memory: A semigroup approach

3This paper is concerned with the asymptotic behavior in time of solutions to a linear problem arising in the theory of heat conduction with memory. In a rigid heat conductor obeying the Gurtin-Pipkin constitutive model for the heat flux, the energy balance leads to an hyperbolic, linear integro-differential equation. In spite of the presence of a convolution term, the homogeneous original problem, subject to initial-history conditions, is transformed into an autonomous system by a suitable choice of variables. By means of semigroup techniques the exponential decay of solutions is provided.restrictedrestrictedGIORGI C.; NASO M.G.; PATA V.Giorgi, Claudio; Naso, MARIA GRAZIA; Pata, V