Exponential decay for the solution of semilinear viscoelastic wave equations with localized damping

By Marcelo Moreira Cavalcanti, N. Cavalcanti, J. A. Soriano. 2002

296 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/84827345f9e44e357f6f1d64f716fbd4aeed5fc6

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1. Wenjun Liu
2. Salim A. Messaoudi
3. Aissa Guesmia
4. B. Said-Houari
5. Irena Lasiecka
6. Xiaojun Wang
7. Mokhtar Kirane
8. M. Al‐Gharabli

Citations in the corpus

• Existence and a general decay results for a viscoelastic plate equation with a logarithmic nonlinearity (2019, background): “Berrimi and Messaoudi [4] established the result of [8], under weaker conditions on both a and g, to a problem where a source term is competing with the damping term.”
• Existence and asymptotic stability of a viscoelastic wave equation with a delay (2011, methodology): “the authors showed an exponential decay result under some geometric restrictions on the subset ω .T he result in [6] has been improved by Berrimi and Messaoudi [4], who showed the same result as in [ 6 ], under weaker conditions on both a and g .I n [3], more general abstract version of Eq. (6) has ”
• 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”
• General decay of the solution for a viscoelastic wave equation with a time-varying delay term in the internal feedback (2012, background): “They improved the result of [7] by establishing exponential stability for g decaying exponentially and h linear and polynomial stability for g decaying polynomially and h nonlinear.”
• Existence and decay of solutions of a viscoelastic equation with a nonlinear source (2006, background): “They improved the result of [5] by establishing exponential stability for g decaying exponentially and h linear and polynomial stability for g decaying polynomially and h nonlinear.”
• Blow up and global existence in a nonlinear viscoelastic wave equation (2003, unknown): “[4] studied (1.”