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Decay of an Extensible Viscoelastic Plate Equation with a Nonlinear Time Delay

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An extensible viscoelastic plate equation with a nonlinear time-varying delay feedback and nonlinear source term is considered. Under suitable assumptions on relaxation function, nonlinear internal delay feedback, and source term,… Click to show full abstract

An extensible viscoelastic plate equation with a nonlinear time-varying delay feedback and nonlinear source term is considered. Under suitable assumptions on relaxation function, nonlinear internal delay feedback, and source term, we establish a general decay of energy by using the multiplier method if the weight of weak dissipation and the delay satisfy $$\mu _2<\frac{\mu _1\alpha _1(1-d)}{\alpha _2(1-\alpha _1d)}$$μ2<μ1α1(1-d)α2(1-α1d), and extend some known results.

Keywords: equation nonlinear; plate equation; viscoelastic plate; delay; nonlinear time; extensible viscoelastic

Journal Title: Bulletin of the Malaysian Mathematical Sciences Society
Year Published: 2018

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