Time-dependent global attractor for extensible Berger equation

Meng, Fengjuan; Wu, Jie; Zhao, Chunxiang

doi:10.1016/j.jmaa.2018.09.050

Cited by 16 publications

(9 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…From the proof of Theorem 3.1, similar to [27], and by Hölder, Young inequalities, we can have By Lemma 3.2, 3.3, from [9], there holds is the contractive function for each fixed T . Further, similar the results in [9,14], we can easily get that φ t T in (4.15) is a contractive function, so ψ t T is asymptotic contractive function, then from (4.15) we know that the process U (t, τ ) is asymptotic contractive process on the whole time-dependent space. The proof is completed.…”

Section: Multiplying the Above Equation By 2ū T And Integrating Oversupporting

confidence: 64%

Attractor of the Kirchhoff type plate equation with memory and nonlinear damping on the whole time-dependent space

Liu¹,

Ma²,

Xu³

2022

DCDS-B

View full text Add to dashboard Cite

<p style='text-indent:20px;'>First of all, by virtue of the Faedo-Galerkin procedure, we obtain existence of solution for the Kirchhoff type plate equation with memory and nonlinear damping on <inline-formula><tex-math id="M1">\begin{document}$ \mathbb{R}^{n}. $\end{document}</tex-math></inline-formula> Secondly, using a new method of asymptotic contractive functions presented in [<xref ref-type="bibr" rid="b9">9</xref>] as well as the tail estimates we prove the asymptotic compactness of solution process. Finally, existence of the time-dependent attractor on <inline-formula><tex-math id="M2">\begin{document}$ \mathbb{R}^{n} $\end{document}</tex-math></inline-formula> is shown. The results are new and they are the extension and improvement of [<xref ref-type="bibr" rid="b9">9</xref>].</p>

show abstract

Section: Multiplying the Above Equation By 2ū T And Integrating Oversupporting

confidence: 64%

Attractor of the Kirchhoff type plate equation with memory and nonlinear damping on the whole time-dependent space

Liu¹,

Ma²,

Xu³

2022

DCDS-B

View full text Add to dashboard Cite

show abstract

“…In regard to the nonlinear damping g(u t ), many people have also extensively studied, see e.g. Kouémou Patcheu [24], Ma and Narciso [20], Cavalcanti [8], Yang [39], Yang and Wang [37], Meng and Wu et al [22] etc., moreover, it is worth mentioning that Chueshov and Lasiecka [10] have considered systematically the long-time behaviour of the second-order abstract equation…”

mentioning

confidence: 99%

The global attractor for a class of extensible beams with nonlocal weak damping

Zhao¹,

Zhao²,

Zhong³

2020

Discrete &Amp; Continuous Dynamical Systems - B

Self Cite

View full text Add to dashboard Cite

The goal of this paper is to study the long-time behavior of a class of extensible beams equation with the nonlocal weak damping utt + ∆ 2 u − m(∇u 2)∆u + ut p ut + f (u) = h, in Ω × R + , p ≥ 0 on a bounded smooth domain Ω ⊂ R n with hinged (clamped) boundary condition. Under some suitable conditions on the Kirchhoff coefficient m(∇u 2) and the nonlinear term f (u), the well-posedness is established by means of the monotone operator theory and the existence of a global attractor is obtained in the subcritical case, where the asymptotic smooothness of the semigroup is verified by the energy reconstruction method.

show abstract

“…Conti et al [16] proved the existence and regularity of a timedependent attractor, and they [18] obtained the asymptotic structure of a time-dependent attractor. Meng et al [21,22] discussed and investigated the longtime dynamical behavior for the semilinear wave equation with nonlinear damping and the extensible Berger equation via a contractive function method, respectively. In addition, Meng et al [20] gave some necessary and sufficient conditions to guarantee the existence of a time-dependent attractor.…”

Section: Introductionmentioning

confidence: 99%

Asymptotic Regularity and Existence of Time-Dependent Attractors for Second-Order Undamped Evolution Equations with Memory

Wang

Gao

2022

Mathematics

View full text Add to dashboard Cite

Our purpose in this article is to study the asymptotic behavior of undamped evolution equations with fading memory on time-dependent spaces. By means of the theory of processes on time-dependent spaces, asymptotic a priori estimate and the technique of operator decomposition and the existence and asymptotic regularity of time-dependent attractors are, respectively, established in the critical case. At the same time, we also obtain the asymptotic regularity of the solution.

show abstract

Time-dependent global attractor for extensible Berger equation

Cited by 16 publications

References 29 publications

Attractor of the Kirchhoff type plate equation with memory and nonlinear damping on the whole time-dependent space

Attractor of the Kirchhoff type plate equation with memory and nonlinear damping on the whole time-dependent space

The global attractor for a class of extensible beams with nonlocal weak damping

Asymptotic Regularity and Existence of Time-Dependent Attractors for Second-Order Undamped Evolution Equations with Memory

Contact Info

Product

Resources

About