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

By Marcelo Moreira Cavalcanti, Valéria N. Domingos Cavalcanti, J. Filho, J. A. Soriano. Differential and Integral Equations, 2001

231 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/eeaadcf0985a7814723a690a0bc7542e8554dd95

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In Computational Theory and Mathematics

In Control and Systems Engineering

Citations in the corpus

Existence and sharp decay rate estimates for a von Karman system with long memory (2015, unknown): “This area of research was followed with a considerably large number of papers published on viscoelasticity and their asymptotic behavior quantized by decay rates obtained for the total energy: [25–28, 35–37,29,30,38,39].”
Existence and decay of solutions of a viscoelastic equation with a nonlinear source (2006, unknown): “[3,4].”
General decay of the solution for a viscoelastic wave equation with a time-varying delay term in the internal feedback (2012, background): “For other related works, we refer the readers to [6, 15, 17, 18, 26, 20, 29, 31, 32, 33] and the references therein.”
Exponential decay of solutions to a viscoelastic equation with nonlinear localized damping. (2004, background): “Introduction Cavalcanti et al [3] studied the equation utt −∆u + ∫ t 0 g(t− τ)∆u(τ)dτ + a(x)ut + |u|γu = 0, in Ω× (0,∞) u(x, t) = 0, x ∈ ∂Ω, t ≥ 0 u(x, 0) = u0(x), ut(x, 0) = u1(x), x ∈ Ω, (1.1) where Ω is a bounded domain of Rn (n ≥ 1) with a smooth boundary ∂Ω, γ > 0, g is a positive function, and”
Blow-up of positive-initial-energy solutions of a nonlinear viscoelastic hyperbolic equation (2006, background): “[5] established an existence result and a decay result for viscoelastic problems with nonlinear boundary damping.”
Exponential decay for the solution of semilinear viscoelastic wave equations with localized damping (2002, methodology): “To end, we would like to mention the works from the authors Cavalcanti, Domingos Cavalcanti, Prates Filho and Soriano [3] in connection with the viscoelastic linear wave equation and nonlinear boundary dissipation and Aassila, Cavalcanti and Soriano [1] concerned with the wave equation subject to vi”