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.

Decay estimates for second order evolution equations with memory / Fatiha Alabau, Boussouira; Piermarco, Cannarsa; Sforza, Daniela. - In: JOURNAL OF FUNCTIONAL ANALYSIS. - ISSN 0022-1236. - ELETTRONICO. - 254:5(2008), pp. 1342-1372. [10.1016/j.jfa.2007.09.012]

Decay estimates for second order evolution equations with memory

SFORZA, Daniela
2008

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.
exponential decay; global existence; integro-differential equations; integrodifferential equations; linear elasticity; nonlinear wave equations; petrovsky system; polynomial decay; stability
01 Pubblicazione su rivista::01a Articolo in rivista
Decay estimates for second order evolution equations with memory / Fatiha Alabau, Boussouira; Piermarco, Cannarsa; Sforza, Daniela. - In: JOURNAL OF FUNCTIONAL ANALYSIS. - ISSN 0022-1236. - ELETTRONICO. - 254:5(2008), pp. 1342-1372. [10.1016/j.jfa.2007.09.012]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/73696
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