Inertial manifold for the motion of strongly damped nonlinear elastic beams

Giselle Bianchi1, Alfredo Marzocchi2
1Dipartimento di Elettronica per l'Automazione, Università degli Studi di Brescia, I-25124 Brescia, Italy, , IT
2Dipartimento di Matematica, Università Cattolica del S. Cuore, I-25121 Brescia, Italy, IT

Tóm tắt

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.