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

Eugenio Cabanillas Lapa

Producción científica: Contribución a una revista › Artículo › revisión exhaustiva

1 Cita (Scopus)

Resumen

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)

Idioma original	Inglés
Páginas (desde-hasta)	171-177
Número de páginas	7
Publicación	Journal of Applied Nonlinear Dynamics
Volumen	11
N.º	1
DOI	https://doi.org/10.5890/JAND.2022.03.010
Estado	Publicada - 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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title = "A Damped Nonlinear Hyperbolic Equation with Nonlinear Strain Term",

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",

year = "2022",

doi = "10.5890/JAND.2022.03.010",

language = "Ingl{\'e}s",

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T1 - A Damped Nonlinear Hyperbolic Equation with Nonlinear Strain Term

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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U2 - 10.5890/JAND.2022.03.010

DO - 10.5890/JAND.2022.03.010

M3 - Artículo

AN - SCOPUS:85120945357

SN - 2164-6457

VL - 11

SP - 171

EP - 177

JO - Journal of Applied Nonlinear Dynamics

JF - Journal of Applied Nonlinear Dynamics

IS - 1

ER -

A Damped Nonlinear Hyperbolic Equation with Nonlinear Strain Term

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