21 research outputs found
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