We consider a strongly damped semilinear equation arising in the theory of elastic beams. We prove the existence of an exponentially attracting finite-dimensional vector space in the Hilbert space of the solutions (a so-called inertial manifold), and provide some numerical estimates of the dimension of the manifold.
Bianchi, G., Marzocchi, A., Inertial manifold for the motion of strongly damped nonlinear elastic beams, <<NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS>>, 1998; 5 (2): 181-192. [doi:10.1007/s000300050041] [https://hdl.handle.net/10807/300020]
Inertial manifold for the motion of strongly damped nonlinear elastic beams
Marzocchi, Alfredo
1998
Abstract
We consider a strongly damped semilinear equation arising in the theory of elastic beams. We prove the existence of an exponentially attracting finite-dimensional vector space in the Hilbert space of the solutions (a so-called inertial manifold), and provide some numerical estimates of the dimension of the manifold.
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