Differential and Integral Equations

Existence and uniform decay rates for viscoelastic problems with nonlinear boundary damping

M. M. Cavalcanti, V. N. Domingos Cavalcanti, J. S. Prates Filho, and J. A. Soriano

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The linear viscoelastic equation is considered. We prove existence and uniform decay rates of the energy by assuming a nonlinear feedback acting on the boundary and provided the relaxation function decays exponentially. The existence is proved by means of the Faedo-Galerkin method, and the asymptotic behaviour is obtained by making use of the multiplier technique combined with integral inequalities due to Komornik.

Article information

Differential Integral Equations, Volume 14, Number 1 (2001), 85-116.

First available in Project Euclid: 21 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35L20: Initial-boundary value problems for second-order hyperbolic equations
Secondary: 35D05 35L70: Nonlinear second-order hyperbolic equations 45K05: Integro-partial differential equations [See also 34K30, 35R09, 35R10, 47G20] 74D10: Nonlinear constitutive equations 74G25: Global existence of solutions


Cavalcanti, M. M.; Domingos Cavalcanti, V. N.; Prates Filho, J. S.; Soriano, J. A. Existence and uniform decay rates for viscoelastic problems with nonlinear boundary damping. Differential Integral Equations 14 (2001), no. 1, 85--116. https://projecteuclid.org/euclid.die/1356123377

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