Existence and decay of solutions of a viscoelastic equation with a nonlinear source

By Said Berrimi, Salim A. Messaoudi. 2006

252 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/5f15cc0c087690f30ccecee26051e65b964ff58a

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In Computational Theory and Mathematics

In Control and Systems Engineering

In Mathematical Physics

Citations in the corpus

General decay of solutions of a nonlinear system of viscoelastic wave equations (2011, background): “For viscoelastic systems, Messaoudi and Tatar [22] considered the following problem ⎧⎪⎪⎨ ⎪⎪⎩ utt − Δu+ ∫ t 0 g (t− s) Δu (x, s) ds+ f(u, v) = 0, x ∈ Ω, t > 0, vtt − Δv + ∫ t 0 h (t− s) Δv (x, s) ds+ k(u, v) = 0, x ∈ Ω, t > 0, (1.7) where the functions f and k satisfying for all (u, v) ∈ R2 the follo”
General decay of the solution for a viscoelastic wave equation with a time-varying delay term in the internal feedback (2012, unknown): “Berrimi and Messaoudi [3] improved Cavalcanti’s result by introducing a different functional which allowed to weak the conditions on both a and g.”
Existence and asymptotic stability of a viscoelastic wave equation with a delay (2011, result): “In fact, the decay rates obtained in [3] are in line with the ones obtained in [ 4 ]f or Eq. (6).”
Intrinsic Decay Rate Estimates for Semilinear Abstract Second Order Equations with Memory (2014, background): “t/ [7–9, 12, 18, 19, 25, 26, 32], there have been few attempts to reach the level of generality which does not require such specifications.”
Decay estimates for second order evolution equations with memory (2008, methodology): “Our first example concerns the semilinear wave equation with memory that was analyzed in [5].”
Existence and sharp decay rate estimates for a von Karman system with long memory (2015, unknown): “There are four main ingredients in the approach developed for the solution to the problem stated above: (i) extensive use of ‘‘sharp regularity’’ of Airy’s stress function [7], (ii) construction and use of multipliers dealing with viscoelasticity and introduced originally in [27] and later used in [”