A Damped Nonlinear Hyperbolic Equation with Nonlinear Strain Term

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Resumen

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)

Idioma originalInglés
Páginas (desde-hasta)171-177
Número de páginas7
PublicaciónJournal of Applied Nonlinear Dynamics
Volumen11
N.º1
DOI
EstadoPublicada - 2022

Nota bibliográfica

Funding Information:
The author would like to thank to the anonymous referees for their constructive comments and suggestions which helped to improve the manuscript

Publisher Copyright:
© 2022. L&H Scientific Publishing, LLC. All rights reserved

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