We establish some new results concerning the exponential decay and the polynomial decay 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∂_tt u(t)-α∆u(t)+β∂_t u(t)+∫_0^t μ(s)∆u(t-s)ds=0describing the motion of linearly viscoelastic solids. We provide sufficient conditions for the decay to hold, without invoking differential inequalities involving the convolution kernel μ.
Uniform decay properties of linear Volterra integro-differential equations / Conti, Monica; Gatti, Stefania; Pata, Vittorino. - In: MATHEMATICAL MODELS AND METHODS IN APPLIED SCIENCES. - ISSN 0218-2025. - STAMPA. - 18:1(2008), pp. 21-45. [10.1142/S0218202508002590]
Uniform decay properties of linear Volterra integro-differential equations
GATTI, Stefania;
2008
Abstract
We establish some new results concerning the exponential decay and the polynomial decay 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∂_tt u(t)-α∆u(t)+β∂_t u(t)+∫_0^t μ(s)∆u(t-s)ds=0describing the motion of linearly viscoelastic solids. We provide sufficient conditions for the decay to hold, without invoking differential inequalities involving the convolution kernel μ.
Pubblicazioni consigliate
I metadati presenti in IRIS UNIMORE sono rilasciati con licenza Creative Commons CC0 1.0 Universal, mentre i file delle pubblicazioni sono rilasciati con licenza Attribuzione 4.0 Internazionale (CC BY 4.0), salvo diversa indicazione.
In caso di violazione di copyright, contattare Supporto Iris
