A Damped Nonlinear Hyperbolic Equation with Nonlinear Strain Term

Eugenio Cabanillas Lapa

doi:10.5890/JAND.2022.03.010

A Damped Nonlinear Hyperbolic Equation with Nonlinear Strain Term

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Abstract

In this work, we investigate an initial boundary value problem related to the nonlinear hyperbolic equation u_tt +u_xxxx+αu_xxxxt = f (u_x)_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 language	English
Pages (from-to)	171-177
Number of pages	7
Journal	Journal of Applied Nonlinear Dynamics
Volume	11
Issue number	1
DOIs	https://doi.org/10.5890/JAND.2022.03.010
State	Published - 2022

Bibliographical note

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

Keywords

Energy functional
Exponential decay
Hyperbolic equation
Nonlinear strain

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10.5890/JAND.2022.03.010

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abstract = "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)",

keywords = "Energy functional, Exponential decay, Hyperbolic equation, Nonlinear strain",

author = "Lapa, {Eugenio Cabanillas}",

note = "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: {\textcopyright} 2022. L&H Scientific Publishing, LLC. All rights reserved",

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AU - Lapa, Eugenio Cabanillas

N1 - 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

PY - 2022

Y1 - 2022

N2 - 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)

AB - 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)

KW - Energy functional

KW - Exponential decay

KW - Hyperbolic equation

KW - Nonlinear strain

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M3 - Artículo

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SN - 2164-6457

VL - 11

SP - 171

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JO - Journal of Applied Nonlinear Dynamics

JF - Journal of Applied Nonlinear Dynamics

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ER -

A Damped Nonlinear Hyperbolic Equation with Nonlinear Strain Term

Abstract

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Keywords

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