We analyze a differential system arising in the theory of isothermal viscoelasticity. This system is equivalent to an integrodifferential equation of hyperbolic type with a cubic nonlinearity, where the dissipation mechanism is contained only in the convolution integral, accounting for the past history of the displacement. In particular, we consider here a convolution kernelwhich entails an extremely weak dissipation. In spite of that,we show that the related dynamical system possesses a globalattractor of optimal regularity.
Attractors for semilinear equations of viscoelasticity with very low dissipation / Gatti, Stefania; Miranville, A; Pata, V; Zelik, S.. - In: ROCKY MOUNTAIN JOURNAL OF MATHEMATICS. - ISSN 0035-7596. - STAMPA. - 38:4(2008), pp. 1117-1138. [10.1216/RMJ-2008-38-4-1117]
Attractors for semilinear equations of viscoelasticity with very low dissipation
GATTI, Stefania;
2008
Abstract
We analyze a differential system arising in the theory of isothermal viscoelasticity. This system is equivalent to an integrodifferential equation of hyperbolic type with a cubic nonlinearity, where the dissipation mechanism is contained only in the convolution integral, accounting for the past history of the displacement. In particular, we consider here a convolution kernelwhich entails an extremely weak dissipation. In spite of that,we show that the related dynamical system possesses a globalattractor of optimal regularity.
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