A Damped Nonlinear Hyperbolic Equation with Nonlinear Strain Term

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In this work, we investigate an initial boundary value problem related to the nonlinear hyperbolic equation utt +uxxxx+αuxxxxt = f (ux)x, for f(s) =|s|ρ +|s|σ,1 < ρ,σ, α > 0. Under suitable conditions, we prove the existence of global solutions and the exponential decay of energy. The nonlinearity f (s) introduces some obstacles in the process of obtaining a priori estimates and we overcome this difficulty by employing an argument due to Tartar (1978). The exponential decay is obtained via an integral inequality introduced by Komornik (1994)

Original languageEnglish
Pages (from-to)171-177
Number of pages7
JournalJournal of Applied Nonlinear Dynamics
Issue number1
StatePublished - 2022

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  • Energy functional
  • Exponential decay
  • Hyperbolic equation
  • Nonlinear strain


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