The main purpose of this work is to study the damping effect of memory terms associated with singular convolution kernels on the asymptotic behavior of the solutions of second order evolution equations in Hilbert spaces. For kernels that decay exponentially at infinity and possess strongly positive definite primitives, the exponential stability of weak solutions is obtained in the energy norm. It is also shown that this theory applies to several examples of kernels with possibly variable sign, and to a problem in nonlinear viscoelasticity. (C) 2011 Elsevier Inc. All rights reserved.
Integro-differential equations of hyperbolic type with positive definite kernels / Piermarco, Cannarsa; Sforza, Daniela. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - ELETTRONICO. - 250:12(2011), pp. 4289-4335. [10.1016/j.jde.2011.03.005]
Integro-differential equations of hyperbolic type with positive definite kernels
SFORZA, Daniela
2011
Abstract
The main purpose of this work is to study the damping effect of memory terms associated with singular convolution kernels on the asymptotic behavior of the solutions of second order evolution equations in Hilbert spaces. For kernels that decay exponentially at infinity and possess strongly positive definite primitives, the exponential stability of weak solutions is obtained in the energy norm. It is also shown that this theory applies to several examples of kernels with possibly variable sign, and to a problem in nonlinear viscoelasticity. (C) 2011 Elsevier Inc. All rights reserved.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
