This paper develops a unified method to derive decay estimates for general second order integro-differential evolution equations with semilinear source terms. Depending on the properties of convolution kernels at infinity, we show that the energy of a mild solution decays exponentially or polynomially as t -> +infinity. Our approach is based on integral inequalities and multiplier techniques. These decay results can be applied to various partial differential equations. We discuss three examples: a semilinear viscoelastic wave equation, a linear anisotropic elasticity model, and a Petrovsky type system. (C) 2007 Elsevier Inc. All rights reserved.

Alabau Boussouira, F., Cannarsa, P., Sforza, D. (2008). Decay estimates for second order evolution equations with memory. JOURNAL OF FUNCTIONAL ANALYSIS, 254(5), 1342-1372 [10.1016/j.jfa.2007.09.012].

Decay estimates for second order evolution equations with memory

CANNARSA, PIERMARCO;
2008-01-01

Abstract

This paper develops a unified method to derive decay estimates for general second order integro-differential evolution equations with semilinear source terms. Depending on the properties of convolution kernels at infinity, we show that the energy of a mild solution decays exponentially or polynomially as t -> +infinity. Our approach is based on integral inequalities and multiplier techniques. These decay results can be applied to various partial differential equations. We discuss three examples: a semilinear viscoelastic wave equation, a linear anisotropic elasticity model, and a Petrovsky type system. (C) 2007 Elsevier Inc. All rights reserved.
2008
Pubblicato
Rilevanza internazionale
Articolo
Sì, ma tipo non specificato
Settore MAT/05 - ANALISI MATEMATICA
English
Con Impact Factor ISI
Exponential decay; Global existence; Integro-differential equations; Linear elasticity; Nonlinear wave equations; Petrovsky system; Polynomial decay; Stability
Alabau Boussouira, F., Cannarsa, P., Sforza, D. (2008). Decay estimates for second order evolution equations with memory. JOURNAL OF FUNCTIONAL ANALYSIS, 254(5), 1342-1372 [10.1016/j.jfa.2007.09.012].
Alabau Boussouira, F; Cannarsa, P; Sforza, D
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/55584
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