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).
@article{2669,
title = {Decadimento uniforme per equazioni integro-differenziali lineari di Volterra},
journal = {Bruno Pini Mathematical Analysis Seminar},
year = {2011},
doi = {10.6092/issn.2240-2829/2669},
language = {IT},
url = {http://dml.mathdoc.fr/item/2669}
}
Gatti, Stefania. Decadimento uniforme per equazioni integro-differenziali lineari di Volterra. Bruno Pini Mathematical Analysis Seminar, (2011), . doi : 10.6092/issn.2240-2829/2669. http://gdmltest.u-ga.fr/item/2669/