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.

Cannarsa, P., Sforza, D. (2011). Integro-differential equations of hyperbolic type with positive definite kernels. JOURNAL OF DIFFERENTIAL EQUATIONS, 250(12), 4289-4335 [10.1016/j.jde.2011.03.005].

Integro-differential equations of hyperbolic type with positive definite kernels

CANNARSA, PIERMARCO;SFORZA, DANIELE
2011-01-01

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.
2011
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/05 - ANALISI MATEMATICA
English
Con Impact Factor ISI
Integro-differential equations; Global existence; Stability; Exponential decay; Weakly singular kernels
Cannarsa, P., Sforza, D. (2011). Integro-differential equations of hyperbolic type with positive definite kernels. JOURNAL OF DIFFERENTIAL EQUATIONS, 250(12), 4289-4335 [10.1016/j.jde.2011.03.005].
Cannarsa, P; Sforza, D
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/102795
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