Atratores para uma classe de equações de vigas extensíveis fracamente dissipativas / Attractors for a class of equations of extensible beams weakly dissipative

AUTOR(ES)
DATA DE PUBLICAÇÃO

2010

RESUMO

This work contains some results on the existence, uniqueness and asymptotic behavior of solutions for a nonlinear beam equation of Kirchhoff type, u IND. tt+ DELTA POT. 2u+ M(INT. IND.|u| 2 dx) u + g(u IND. t) + f (u) = h; where R POT. Nis a bounded domain with smooth boundary . This equation is a model for small vibrations of extensible beams. The nonlocal term M(INT. IND.|u| 2 dx) u is related to the variation of tensions in the beam due to its extensibility. The term f (u IND. t) represents a damping mechanism for the system and g(u) represents the force exerted by the foundation. The function h represents an additional external force. We consider the problem with boundary condition u|×R+ = u SUP. |×R+ = 0, which corresponds to the model of clamped beams. We discuss the cases where the dissipation is linear and the case nonlinear. We show that in both cases, the dynamical system associated to the problem has a global attractor. However, when the dissipation is linear, we obtain, in a more regular space, the existence of an inertial set of finite dimension, which attracts exponentially all bounded sets of this space

ASSUNTO(S)

berger-kirchhoff equation atrator exponencial exponential attractor global attractor atrator global equação berger-kirchhoff

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