Bounds for Blow-up Time to a Viscoelastic Hyperbolic Equation of Kirchhoff Type with Variable Sources

Liao, Menglan; Guo, Bao‐Zhu; Zhu, Xiangyu

doi:10.1007/s10440-020-00357-3

Cited by 10 publications

(4 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The study of these systems is based on the use of the Lebesgue and Sobolev spaces with variable exponents (see for instance [15,14,40]). More details on these problems can be found in previous studies [30,34,32,31,33,35,36,38,37,43,44,45] and references therein.…”

Section: Introductionmentioning

confidence: 99%

General decay of a nonlinear viscoelastic wave equation with Balakrishn\^{a}n-Taylor damping and a delay involving variable source

rahmoune,

Zuo

2024

Preprint

View full text Add to dashboard Cite

This paper is devoted to the stability of a viscoelastic problem with Balakrishn\^{a}n-Taylor damping and time delay involving variable-exponent nonlinearity. Under some assumptions on the relaxation function, we establish the general decay estimate for the energy via suitable Lyapunov functionals. The problem considered is novel and meaningful because the presence of the flutter panel equation and the spillover problem with memory and variable exponents time delay control. Our result generalizes and improves previous conclusion in the literature.

show abstract

Section: Introductionmentioning

confidence: 99%

General decay of a nonlinear viscoelastic wave equation with Balakrishn\^{a}n-Taylor damping and a delay involving variable source

rahmoune,

Zuo

2024

Preprint

View full text Add to dashboard Cite

show abstract

“…In particular, PDEs concerning Kirchhoff terms and variable exponent have attracted the attention of researchers, e.g. [3,7,8,12,14,15,18,25,35].…”

Section: Introductionmentioning

confidence: 99%

Asymptotic behavior of solutions for a new general class of parabolic Kirchhoff type equation with variable exponent sources

Chuong

Nhan

Trường

2023

Journal of Mathematical Analysis and Applications

View full text Add to dashboard Cite

“…In particular, PDEs concerning Kirchhoff terms and variable exponent have attracted the attention of researchers, e.g. [3,7,8,12,14,15,18,25,35].…”

Section: Introductionmentioning

confidence: 99%

Asymptotic behavior of solutions for a new general class of parabolic Kirchhoff type equation with variable exponent sources

Quach

Nhan

2022

Preprint

View full text Add to dashboard Cite

In this paper, we study the following problem:\begin{align*} \begin{cases} \displaystyle u_t -M\left(\int_{\Omega}\frac{\left|\nabla u\right|^{p(x)}}{p(x)}\diff x\right)\Delta_{p(x)}u = \left|u\right|^{m(x)-2}u,& (x,t)\in \Omega\times (0,T),\\ u(x,t)=0,&(x,t)\in \partial\Omega\times (0,T),\\ u(x,0)=u_0(x),&x\in \Omega, \end{cases}\end{align*}where $\Omega\subset\mathbb{R}^N$ is a bounded domain with smooth boundary $\partial\Omega$, the functions $p,m:\bar{\Omega}\to\mathbb{R}$ and the Kirchhoff function $M:[0,\infty)\to [0,\infty)$ are specified below. We give a new class of general Kirchhoff function which covers both non-degenerate and degenerate cases, and investigate its effects on the existence and non-existence of global weak solutions to \eqref{1.1} in case the initial energy is subcritical. Moreover, we also give the decay estimate for the energy functional in the former case and an upper bound for the maximal existence time in the latter case. This is a continue working on Nhan et al., [Nonlinear Anal. Real World Appl., 56 (2020), 103155] and also an affirmative answer for the comments by Guo et al., [J. Differential Equation., 340 (2022), 45-82.] 2010 MSC: 35A01, 35B44, 35K55

show abstract

Bounds for Blow-up Time to a Viscoelastic Hyperbolic Equation of Kirchhoff Type with Variable Sources

Cited by 10 publications

References 20 publications

General decay of a nonlinear viscoelastic wave equation with Balakrishn\^{a}n-Taylor damping and a delay involving variable source

General decay of a nonlinear viscoelastic wave equation with Balakrishn\^{a}n-Taylor damping and a delay involving variable source

Asymptotic behavior of solutions for a new general class of parabolic Kirchhoff type equation with variable exponent sources

Asymptotic behavior of solutions for a new general class of parabolic Kirchhoff type equation with variable exponent sources

Contact Info

Product

Resources

About