Global Existence of Weak Solutions for a Logarithmic Wave Equation Arising From Q-Ball Dynamics

Han, Xiaosen

doi:10.4134/bkms.2013.50.1.275

Cited by 70 publications

(39 citation statements)

References 20 publications

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“…According to logarithmic Sobolev inequality and by using Galerkin method combined with compact theorem, similar to the proof in ( [16,[18][19][20][21]), we have the following result.…”

Section: Global Existence In Timementioning

confidence: 72%

Viscoelastic Wave Equation with Logarithmic Nonlinearities in ℝ<sup>n</sup>

Bouhali¹,

Ellaggoune²

2017

JPDE

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Abstract.In any spaces dimension, we use weighted spaces to establish a general decay rate of solution of viscoelastic wave equation with logarithmic nonlinearities. Furthermore, we establish, under convenient hypotheses on g and the initial data, the existence of weak solution associated to the equation. AMS Subject Classifications: 35L05, 35L71, 35B35Chinese Library Classifications: O175.13, O175.27, O175.29

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“…According to logarithmic Sobolev inequality and by using Galerkin method combined with compact theorem, similar to the proof in ( [16,[18][19][20][21]), we have the following result.…”

Section: Global Existence In Timementioning

confidence: 72%

Viscoelastic Wave Equation with Logarithmic Nonlinearities in ℝ<sup>n</sup>

Bouhali¹,

Ellaggoune²

2017

JPDE

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“…A numerical research was given in that work. For the initial boundary value problem of (1.5), Han [11] obtained the global existence of weak solution in R 3 , and Zhang et al [33] proved the decay estimate of energy for this problem in finite dimensional case. In [13], the authors studied logarithmic Boussinesq-type equation, and got the global existence and exponential growth of the solution in the potential well under sub-critical initial energy (E(0) < d).…”

Section: Introductionmentioning

confidence: 99%

Global existence and blow up of solution for semi-linear hyperbolic equation with the product of logarithmic and power-type nonlinearity

Lian¹,

Ahmed²,

Xu³

2020

Opuscula Math.

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In this paper we consider the semilinear wave equation with the multiplication of logarithmic and polynomial nonlinearities. We establish the global existence and finite time blow up of solutions at three different energy levels (\(E(0)\lt d\), \(E(0)=d\) and \(E(0)\gt 0\)) using potential well method. The results in this article shed some light on using potential wells to classify the solutions of the semilinear wave equation with the product of polynomial and logarithmic nonlinearity.

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“…However, there was no theoretical analysis for the problem. In [24], Han proved the global existence of weak solutions, for all…”

Section: Introductionmentioning

confidence: 99%

Global Existence of Solutions for the Viscoelastic Kirchhoff Equation with Logarithmic Source Terms

2020

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In this paper, a nonlinear viscoelastic Kirchhoff equation in a bounded domain with a time-varying delay term and logarithmic nonlinearity in the weakly nonlinear internal feedback is considered, where the global and local existence of solutions in suitable Sobolev spaces by means of the energy method combined with Faedo-Galerkin procedure is proved with respect to the condition of the weight of the delay term in the feedback and the weight of the term without delay and the speed of delay. Furthermore, a general stability estimate using some properties of convex functions is given. These results extend and improve many results in the literature.

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Global Existence of Weak Solutions for a Logarithmic Wave Equation Arising From Q-Ball Dynamics

Abstract: Abstract. In this paper we investigate an initial boundary value problem of a logarithmic wave equation. We establish the global existence of weak solutions to the problem by using Galerkin method, logarithmic Sobolev inequality and compactness theorem.

Cited by 70 publications

References 20 publications

Viscoelastic Wave Equation with Logarithmic Nonlinearities in ℝ<sup>n</sup>

Viscoelastic Wave Equation with Logarithmic Nonlinearities in ℝ<sup>n</sup>

Global existence and blow up of solution for semi-linear hyperbolic equation with the product of logarithmic and power-type nonlinearity

Global Existence of Solutions for the Viscoelastic Kirchhoff Equation with Logarithmic Source Terms

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