A semilinear partial differential equation of hyperbolic type with a convolution term describing simple viscoelastic materials with fading memory is considered. Regarding the past history (memory) of the displacement as a new variable, the equation is transformed into a dynamical system in a suitable Hilbert space. The dissipation is extremely weak, and it is all contained in the memory term. Longtime behavior of solutions is analyzed. In particular, in the autonomous case, the existence of a global attractors for solutions is achieved.

Global attractors for a semi-linear hyperbolic equation in viscoelasticity

GIORGI, Claudio;PATA, Vittorino
2001-01-01

Abstract

A semilinear partial differential equation of hyperbolic type with a convolution term describing simple viscoelastic materials with fading memory is considered. Regarding the past history (memory) of the displacement as a new variable, the equation is transformed into a dynamical system in a suitable Hilbert space. The dissipation is extremely weak, and it is all contained in the memory term. Longtime behavior of solutions is analyzed. In particular, in the autonomous case, the existence of a global attractors for solutions is achieved.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11379/20092
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