WIAS Preprint No. 1139, (2006)
Attractors for semilinear equations of viscoelasticity with very low dissipation
Authors
- Gatti, Stefania
- Miranville, Alain
- Pata, Vittorino
- Zelik, Sergey
2010 Mathematics Subject Classification
- 35B40 35L70 37L45 45K05 74D99
Keywords
- Hyperbolic equation with memory, dynamical system, Lyapunov function, gradient system, global attractor
DOI
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 kernel which entails an extremely weak dissipation. In spite of that, we show that the related dynamical system possesses a global attractor of optimal regularity.
Appeared in
- Rocky Mountain J. Math., 38 (2008) pp. 1117-1138
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