Exponential decay of solutions to a viscoelastic equation with nonlinear localized damping.

By Said Berrimi, Salim A. Messaoudi. 2004

150 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/69727e583ec21e590fe3ea8408caa0bb39f7d1bd

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

1. Wenjun Liu
2. Said Berrimi
3. Salim A. Messaoudi
4. Muhammad I. Mustafa

Citations in the corpus

• Global existence and uniform stability of solutions for a quasilinear viscoelastic problem (2007, background): “Messaoudi S.A., Blow up and global existence in a nonlinear viscoelastic wave equation, Mathematische Nachrichten Vol. 260 (2003), 58-66.”
• 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.”
• Existence and decay of solutions of a viscoelastic equation with a nonlinear source (2006, background): “[17] S.A. Messaoudi, Decay of the solution energy for a nonlinearly damped wave equation, Arab.”
• Blow-up of positive-initial-energy solutions of a nonlinear viscoelastic hyperbolic equation (2006, methodology): “This work was later improved by Cavalcanti et al. [6] and Berrimi and Messaoudi [ 2 ] using different methods.”
• ASYMPTOTIC BEHAVIOR FOR A VISCOELASTIC WAVE EQUATION WITH A DELAY TERM (2013, unknown): “This result was later extended by Berrimi and Messaoudi [2] to the nonlinear damping case by introducing a new a functional, they weakened the conditions in a(x) and g(t) and obtained the decay result.”
• General decay of the solution for a viscoelastic wave equation with a time-varying delay term in the internal feedback (2012, background): “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 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 [”