Abstract
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.
Citation
M. M. Cavalcanti. V. N. Domingos Cavalcanti. J. S. Prates Filho. J. A. Soriano. "Existence and uniform decay rates for viscoelastic problems with nonlinear boundary damping." Differential Integral Equations 14 (1) 85 - 116, 2001. https://doi.org/10.57262/die/1356123377
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