Global solutions and exponential decay to a Klein–Gordon equation of Kirchhoff-Carrier type with strong damping and nonlinear logarithmic source term

Global solutions and exponential decay to a Klein–Gordon equation of Kirchhoff-Carrier type with strong damping and nonlinear logarithmic source term

This paper is concerned with the existence and exponential stability of the global solution to a Klein–Gordon equation of Kirchhoff-Carrier type with strong damping −Δutand logarithmic source term uln|u|R2. We apply the potential well corresponding to the logarithmic nonlinearity. We prove the globa...

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Main Authors: S.M.S. Cordeiro, D.C. Pereira, J. Ferreira, C.A. Raposo
Format: Article
Language:English
Published: Elsevier 2021-06-01
Series:Partial Differential Equations in Applied Mathematics
Subjects:
Klein–Gordon equation
Global weak solution
Asymptotic behavior
Logarithmic source term
Online Access:http://www.sciencedirect.com/science/article/pii/S2666818120300188
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spelling doaj-88a2b8172ad949c4873c4348ef2409252021-06-05T06:10:57ZengElsevierPartial Differential Equations in Applied Mathematics2666-81812021-06-013100018Global solutions and exponential decay to a Klein–Gordon equation of Kirchhoff-Carrier type with strong damping and nonlinear logarithmic source termS.M.S. Cordeiro0D.C. Pereira1J. Ferreira2C.A. Raposo3Faculty of Exact Sciences and Technology, Federal University of Pará, 68440-000, Abaetetuba, Pará, BrazilDepartment of Mathematics, State University of Pará, 66113-200, Belém, Pará, BrazilDepartment of Exact Sciences, Federal Fluminense University, 27213-145, Volta Redonda, Rio de Janeiro, BrazilDepartment of Mathematics, Federal University of São João del-Rei, 36307-352, São João del-Rei, Minas Gerais, Brazil; Corresponding author.This paper is concerned with the existence and exponential stability of the global solution to a Klein–Gordon equation of Kirchhoff-Carrier type with strong damping −Δutand logarithmic source term uln|u|R2. We apply the potential well corresponding to the logarithmic nonlinearity. We prove the global weak solutions and the exponential stability for initial data in the set of stability created from the Nehari Manifold.http://www.sciencedirect.com/science/article/pii/S2666818120300188Klein–Gordon equationGlobal weak solutionAsymptotic behaviorLogarithmic source term
collection DOAJ
language English
format Article
sources DOAJ
author S.M.S. Cordeiro
D.C. Pereira
J. Ferreira
C.A. Raposo
spellingShingle S.M.S. Cordeiro
D.C. Pereira
J. Ferreira
C.A. Raposo
Global solutions and exponential decay to a Klein–Gordon equation of Kirchhoff-Carrier type with strong damping and nonlinear logarithmic source term
Partial Differential Equations in Applied Mathematics
Klein–Gordon equation
Global weak solution
Asymptotic behavior
Logarithmic source term
author_facet S.M.S. Cordeiro
D.C. Pereira
J. Ferreira
C.A. Raposo
author_sort S.M.S. Cordeiro
title Global solutions and exponential decay to a Klein–Gordon equation of Kirchhoff-Carrier type with strong damping and nonlinear logarithmic source term
title_short Global solutions and exponential decay to a Klein–Gordon equation of Kirchhoff-Carrier type with strong damping and nonlinear logarithmic source term
title_full Global solutions and exponential decay to a Klein–Gordon equation of Kirchhoff-Carrier type with strong damping and nonlinear logarithmic source term
title_fullStr Global solutions and exponential decay to a Klein–Gordon equation of Kirchhoff-Carrier type with strong damping and nonlinear logarithmic source term
title_full_unstemmed Global solutions and exponential decay to a Klein–Gordon equation of Kirchhoff-Carrier type with strong damping and nonlinear logarithmic source term
title_sort global solutions and exponential decay to a klein–gordon equation of kirchhoff-carrier type with strong damping and nonlinear logarithmic source term
publisher Elsevier
series Partial Differential Equations in Applied Mathematics
issn 2666-8181
publishDate 2021-06-01
description This paper is concerned with the existence and exponential stability of the global solution to a Klein–Gordon equation of Kirchhoff-Carrier type with strong damping −Δutand logarithmic source term uln|u|R2. We apply the potential well corresponding to the logarithmic nonlinearity. We prove the global weak solutions and the exponential stability for initial data in the set of stability created from the Nehari Manifold.
topic Klein–Gordon equation
Global weak solution
Asymptotic behavior
Logarithmic source term
url http://www.sciencedirect.com/science/article/pii/S2666818120300188
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AT jferreira globalsolutionsandexponentialdecaytoakleingordonequationofkirchhoffcarriertypewithstrongdampingandnonlinearlogarithmicsourceterm
AT caraposo globalsolutionsandexponentialdecaytoakleingordonequationofkirchhoffcarriertypewithstrongdampingandnonlinearlogarithmicsourceterm
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