This work is focused on the equation $$\partial_{tt} u+\partial_{xxxx}u +\int_0^\infty \mu(s) \partial_{xxxx}[u(t)-u(t-s)]ds- \big(\beta+\|\partial_x u\|_{L^2(0,1)}^2\big)\partial_{xx}u= f$$ describing the motion of an extensible viscoelastic beam. Under suitable boundary conditions, the related dynamical system in the history space framework is shown to possess a global attractor of optimal regularity. The result is obtained by exploiting an appropriate decomposition of the solution semigroup, together with the existence of a Lyapunov functional.

Global attractor for an extensible viscoelastic beam

GIORGI, Claudio;PATA, Vittorino;VUK, Elena
2007-01-01

Abstract

This work is focused on the equation $$\partial_{tt} u+\partial_{xxxx}u +\int_0^\infty \mu(s) \partial_{xxxx}[u(t)-u(t-s)]ds- \big(\beta+\|\partial_x u\|_{L^2(0,1)}^2\big)\partial_{xx}u= f$$ describing the motion of an extensible viscoelastic beam. Under suitable boundary conditions, the related dynamical system in the history space framework is shown to possess a global attractor of optimal regularity. The result is obtained by exploiting an appropriate decomposition of the solution semigroup, together with the existence of a Lyapunov functional.
2007
9788889720691
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11379/13977
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