Frictional versus Viscoelastic Damping in a Semilinear Wave Equation

By Marcelo Moreira Cavalcanti, H. P. Oquendo. SIAM Journal of Control and Optimization, 2003

402 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/8200d22fbe30491a4a25bb2aad5bacea067fa347

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Citations in the corpus

Moore-Gibson-Thompson equation with memory, part II: general decay of energy (2015, neutral): “For instance, while the frictional damping alone causes exponential decay; only polynomial decay can be reached when an additional memory term presents itself with a polynomial kernel[7].”
Attractors for wave equations with degenerate memory (2016, methodology): “This was firstly considered in Cavalcanti and Portillo Oquendo [11] to recover the full damping effect from a combined frictional–viscoelastic dissipation.”
General decay of solutions of a nonlinear system of viscoelastic wave equations (2011, methodology): “44, 1–14 (2002) [8] Cavalcanti, M.M., Oquendo, H.P.: Frictional versus viscoelastic damping in a semilinear wave equation.”
Existence and sharp decay rate estimates for a von Karman system with long memory (2015, neutral): “More recently some (not so many) results related on locally distributed viscoelastic effects, (where the concept of propagation of the damping becomes critical) can be found in [40–42] and the most recent work in this direction [43].”
Decay estimates for second order evolution equations with memory (2008, methodology): “Both papers [5] and [8] use a Lyapunov type technique for some perturbed energy, following the method introduced by Komornik and Zuazua [17].”
Global existence and uniform stability of solutions for a quasilinear viscoelastic problem (2007, background): “They established a local existence result and showed, under weaker conditions than those in [3] and [5], that the local solution is global and decays uniformly if the initial data are small enough.”
On the stabilization of the Timoshenko system by a weak nonlinear dissipation (2009, result): “Cavalcanti MM, Oquendo HP. Frictional versus viscoelastic damping in a semilinear wave equation.”
Exponential decay of solutions to a viscoelastic equation with nonlinear localized damping. (2004, methodology): “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, methodology): “[6] and Berrimi and Messaoudi [2] using different methods.”
General decay of the solution for a viscoelastic wave equation with a time-varying delay term in the internal feedback (2012, background): “They showed, under weaker conditions than those in [8], that the solution is global and decay in a polynomial or exponential fashion when the initial data is small enough.”
Existence and a general decay results for a viscoelastic plate equation with a logarithmic nonlinearity (2019, background): “Similar to Cavalcanti and Oquendo [10], we can easily have the following lemma: Lemma 5.3.”