具有时间依赖记忆核的粘弹性方程的吸引子
Attractors for the Viscoelastic Equationwith Time-Dependent Memory Kernel
DOI: 10.12677/PM.2022.127122, PDF, HTML,    国家自然科学基金支持
作者: 袁海燕, 汪 璇*：西北师范大学数学与统计学院，甘肃 兰州
关键词: 粘弹性方程；时间依赖记忆核；时间依赖全局吸引子；Viscoelastic Equation； Time-Dependent Memory Kernel； Time-Dependent Global Attractors
摘要: 对于具有时间依赖记忆核的粘弹性方程，本文研究了该方程解的长时间动力学行为。 当非线性项 f 的增长指数 p 满足1≤p≤5时，在新的理论框架下，利用积分估计方法得到了解的适定性。 同时，当 p 满足1≤p<5时，证明了时间依赖全局吸引子的存在性以及不变性。
Abstract: In this paper, we investigate the long-time dynamical behavior of solutions for the viscoelastic equation with time-dependent memory kernel. When the growth exponent p of nonlinearity f(u) is up to 1≤p≤5, the well-posedness of the solutions is proved by using the integral estimation method, and we obtained an invariant time-dependent global attractor when 1≤p<5 .
文章引用：袁海燕, 汪璇. 具有时间依赖记忆核的粘弹性方程的吸引子[J]. 理论数学, 2022, 12(7): 1103-1124. https://doi.org/10.12677/PM.2022.127122

参考文献

[1] Cavalcanti, M.M., Cavalcanti, V. and Ferreira, J. (2001) Existence and Uniform Decay for a Non-Linear Viscoelastic Equation with Strong Damping. Mathematical Methods in the Applied Sciences, 24, 1043-1053. [Google Scholar] [CrossRef] 
[2] Dafermos, C.M. (1970) Asymptotic Stability in Viscoelasticity. Archive for Rational Mechanics Analysis, 37, 297-308. [Google Scholar] [CrossRef] 
[3] Liu, W. (2009) Uniform Decay of Solutions for a Quasilinear System of Viscoelastic Equations. Nonlinear Analysis, 71, 2257-2267. [Google Scholar] [CrossRef] 
[4] Qin, Y.M., Zhang, J.P. and Sun, L.L. (2013) Upper Semicontinuity of Pullback Attractors for a Non- Autonomous Viscoelastic Equation. Applied Mathematics and Computation, 223, 362-376.[CrossRef] 
[5] Qin, Y., Feng, B. and Zhang, M. (2014) Uniform Attractors for a Non-Autonomous Viscoelastic Equation with a Past History. Nonlinear Analysis Theory Methods Applications, 101, 1-15. [Google Scholar] [CrossRef] 
[6] Aracjo, R.O., Ma, T.F. and Qin, Y.M. (2013) Long-Time Behavior of a Quasilinear Viscoelastic Equation with Past History. Journal of Differential Equations, 254, 4066-4087. [Google Scholar] [CrossRef] 
[7] Messaoudi, S.A. (2008) General Decay of Solutions of a Viscoelastic Equation. Arabian Journal for Science and Engineering, 36, 1457-1467. [Google Scholar] [CrossRef] 
[8] Conti, M., Danese, V., Giorgi, C. and Pata, V. (2018) A Model of Viscoelasticity with Time-Dependent Memory Kernels. American Journal of Mathematical, 140, 349-389. [Google Scholar] [CrossRef] 
[9] Conti, M., Danese, V. and Pata, V. (2018) Viscoelasticity with Time-Dependent Memory Kernels, Part II: Asymptotic behavior of Solutions. American Journal of Mathematical, 140, 1687-1729. [Google Scholar] [CrossRef] 
[10] Pata, V. and Squassina, M. (2005) On the Strongly Damped Wave Equation. Communications in Mathe- matical Physics, 253, 511-533. [Google Scholar] [CrossRef] 
[11] Yang, L. and Wang, X. (2017) Existence of Attractors for the Non-Autonomous Berger Equation with Nonlinear Damping. Electronic Journal of Differential Equations, 2017, 1-14.
[12] Conti, M., Pata, V. and Teman, R. (2013) Attractors for the Processes on Time-Dependent Spaces. Applications to Wave Equations. Journal of Differential Equations, 255, 1254-1277. [Google Scholar] [CrossRef] 
[13] Meng, F.J., Wu, J. and Zhao, C.X. (2019) Time-Dependent Global Attractor for Extensible Berger Equation. Journal of Mathematical Analysis and Applications, 469, 1045-1069. [Google Scholar] [CrossRef] 
[14] Conti, M. and Pata, V. (2014) Asymptotic Structure of the Attractor for Processes on Time-Dependent Spaces. Nonlinear Analysis: Real World Applications, 19, 1-10. [Google Scholar] [CrossRef] 

为你推荐