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

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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