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

Cordeiro, Sebastião Martins Siqueira; Pereira, Ducival Carvalho; Ferreira, J.; Raposo, Carlos A.

doi:10.1016/j.padiff.2020.100018

Cited by 9 publications

(8 citation statements)

References 14 publications

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“…Our numerical results show, for the solutions defined on the one and two dimensional spacial domains (T d , d = 1, 2), that E(ψ) and Q(θ ) converge to the same limit (Figs. 1,2) and that E(φ) decays exponentially to zero (Figs. 3, 4) regardless of the assumptions of Theorem 3.2 made on the initial data ψ 0 , ψ 1 .…”

Section: Discussionmentioning

confidence: 97%

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Energy asymptotics for the strongly damped Klein–Gordon equation

Mohamad

2022

Partial Differ. Equ. Appl.

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We consider the strongly damped Klein–Gordon equation for defocusing nonlinearity and we study the asymptotic behaviour of the energy for periodic solutions. We prove first the exponential decay to zero for zero mean solutions. Then, we characterize the limit of the energy, when the time tends to infinity, for solutions with small enough initial data and we finally prove that such limit is not necessary zero.

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Section: Discussionmentioning

confidence: 97%

“…λ 1 is the first eigenvalue of the operator− under the homogeneous Dirichlet boundary conditions. Considering a functional setting similar to that used in [8], Cordeiro et al [2] proved the exponential decay to zero of the energy related to the strongly damped (L = − ) Klein-Gordon equation of Kirchhoff-Carrier type…”

Section: Introductionmentioning

confidence: 99%

Energy asymptotics for the strongly damped Klein–Gordon equation

Mohamad

2022

Partial Differ. Equ. Appl.

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“…Below, we cite a few. [9] studied the existence and exponential stability of the global solution to a Klein-Gordon equation of Kirchhoff-Carrier type with strong damping and logarithmic source term. An extensible beam equation of Kirchhoff type with internal damping and source term was investigated in [22].…”

Section: Introductionmentioning

confidence: 99%

Global existence and asymptotic behavior for a Timoshenko system with internal damping and logarithmic source terms

et al. 2022

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This manuscript deals with a Timoshenko system with damping and source. The existence and stability of the solution are analyzed taking into account the competition of the internal damping versus the logarithmic source. We use the potential well theory. For initial data in the stability set created by the Nehari surface, the existence of global solutions is proved using Faedo–Galerkin’s approximation. The exponential decay is given by the Nakao theorem. A numerical approach is presented to illustrate the results obtained.

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“…Considering a functional setting similar to that used in [15] , S.M.S. Cordeiro et al [2] proved the exponential decay to zero of the energy related to the strongly damped (L = −∆) Klein-Gordon equation of Kirchhoff-Carrier type…”

Section: Introductionmentioning

confidence: 99%

Energy asymptotics for the strongly damped Klein-Gordon equation

Mohamad¹

2022

Preprint

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We consider the strongly damped Klein Gordon equation for defocusing nonlinearity and we study the asymptotic behaviour of the energy for periodic solutions. We prove first the exponential decay to zero for zero mean solutions. Then, we characterize the limit of the energy, when the time tends to infinity, for solutions with small enough initial data and we finally prove that such limit is not necessary zero.

show abstract

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

Cited by 9 publications

References 14 publications

Energy asymptotics for the strongly damped Klein–Gordon equation

Energy asymptotics for the strongly damped Klein–Gordon equation

Global existence and asymptotic behavior for a Timoshenko system with internal damping and logarithmic source terms

Energy asymptotics for the strongly damped Klein-Gordon equation

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