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Author: Pata, Vittorino × Subject: global attractor ×

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    Attractors for semilinear equations of viscoelasticity with very low disspation
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2006) Gatti, Stefania; Miranville, Alain; Pata, Vittorino; Zelik, Sergey
    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.
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    A remark on the weakly damped wave equation
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2006) Pata, Vittorino; Zelik, Sergey
    In this short note we present a direct method to establish the optimal regularity of the attractor for the semilinear damped wave equation with a nonlinearity of critical growth.