Global Attractors for an Extensible Thermoelastic Beam System

Details Global Attractors for an Extensible Thermoelastic Beam System Global Attractors for an Extensible Thermoelastic Beam System

2009-01-27

arxiv.org/abs/0901.4194v1

Mathematics

Dynamical Systems

21 pages, no figure

Scientific paper

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.

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