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Decadimento uniforme per equazioni integro-differenziali lineari di Volterra

Author(s): Stefania Gatti

Journal: Bruno Pini Mathematical Analysis Seminar
ISSN 2240-2829

Volume: 2;
Issue: 1;
Date: 2011;
Original page

This talk is devoted to some recent results concerning the exponential and the polynomial decays of the energy associated with a linear Volterra integro-differential equation of hyperbolic type in a Hilbert space, which is an abstract version of the equation describing the motion of a linearly viscoelastic solid occupying a (bounded) volume at rest.We provide sufficient conditions for the decay to hold, without invoking differential inequalities involving the convolution kernel. A similar analysis is carried on in the whole N-dimensional real space, although both the polynomial and the exponential decay of the memory kernel lead to a polynomial decay of the energy, with a rate influenced by the space dimension N. These results are contained in two joint papers with Monica Conti and Vittorino Pata (Politecnico di Milano).
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