Differential and Integral Equations
- Differential Integral Equations
- Volume 14, Number 1 (2001), 85-116.
Existence and uniform decay rates for viscoelastic problems with nonlinear boundary damping
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.
Differential Integral Equations, Volume 14, Number 1 (2001), 85-116.
First available in Project Euclid: 21 December 2012
Permanent link to this document
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