ZHANG Tieyuan,DU Xianyun.Existence of Periodic Solution of Plate Equation with Linear Memory[J].Journal of Chengdu University of Information Technology,2022,37(06):730-736.[doi:10.16836/j.cnki.jcuit.2022.06.018]
具有线性记忆项Plate方程周期解的存在性
- Title:
- Existence of Periodic Solution of Plate Equation with Linear Memory
- 文章编号:
- 2096-1618(2022)06-0730-07
- Keywords:
- memory term; plate equation; periodic solution; applied mathematics; infinite dimensional dynamic system
- 分类号:
- O175.29
- 文献标志码:
- A
- 摘要:
- 考虑一类具有线性记忆项的二维plate方程在有界域上周期解的存在性。应用Leray-Schauder不动点定理验证具有线性记忆项plate方程近似周期解的存在,再在其工作空间内验证近似周期解的收敛性,从而得到具有线性记忆项plate方程周期解的存在性。
- Abstract:
- Consider the existence of periodic solutions in a bounded domain of a two-dimensional plate equation with linear memory terms. The Leray-Schauder fixed point theorem is used to verify the existence of the approximate periodic solution of the plate equation with linear memory term, and then the convergence of the approximate solution is verified in its working space, so as to obtain the existence of the periodic solution of the plate equation with linear memory term.
参考文献/References:
[1] Kato H.Existence of Periodic Solutions of the Navier-Stokes Equations[J].Journal of Mathematical Analysis & Applications,1997,208(1):141-157.
[2] Guo B,Du X.Existence of the Periodic Solution for the Weakly Damped Schrödinger-Boussinesq Equation[J].Journal of Mathematical Analysis and Applications,2001,262(2):453-472.
[3] 罗维.大气原始方程组时间周期解的存在性[D].成都:成都信息工程大学,2019.
[4] Woinowsky Krieger S.The Effect of an Axial Force on the Vibration of Hinged Bars[J].J.Appl.Mech,1950,17(1):35-36.
[5] Berger H M.A new approach to the analysis of large deflections of plates[J].Appl.Mech,1955,22:465-472.
[6] Niu L,Zhang J.Existence of global attractors for the nonlinear plate equation with memory term[J].Mathematical Problems in Engineering,2012.
[7] Temam R.Infinite-dimensional dynamical systems in mechanics and physics[M].Springer Science & Business Media,2012.
[8] Grasselli M,Pata V.Robust exponential attractors for a phase-field system with memory[J].Journal of Evolution Equations,2005,5(4):465-483.
备注/Memo
收稿日期:2021-11-17