一类带记忆和非经典耗散项的发展方程的适定性
The Well-Posedness of a Memory-Type Evolution Equation with Nonclassical Dissipation
DOI: 10.12677/PM.2021.118173, PDF, HTML,   
作者: 刘西盟*, 刘 迪, 张江卫：长沙理工大学, 数学与统计学院, 湖南 长沙
关键词: 发展方程；记忆项；非经典耗散；适定性；Evolution Equation； Memory； Nonclassical Dissipation； Well-Posedness
摘要: 本文主要讨论带非经典耗散的记忆型发展方程的适定性问题, 我们运用非经典的 Galerkin 方法及分析技巧得到了弱解的存在性, 同时证明了解的唯一性和对初值的连续依赖性
Abstract: In this paper, we mainly discuss the well-posedness problem of a Memory-type Evolution Equation with nonclassical dissipation. The existence of weak solution is obtained by using the Galerkin’s method and analytical techniques. Also, we prove the uniqueness of the solution and the continuous dependence on initial value.
文章引用：刘西盟, 刘迪, 张江卫. 一类带记忆和非经典耗散项的发展方程的适定性[J]. 理论数学, 2021, 11(8): 1546-1558. https://doi.org/10.12677/PM.2021.118173

参考文献

[1] 张素丽, 张建文, 王海燕. 一类具记忆项拟线性波动方程方程的整体吸号子[J]. 应用数学, 2020, 33(4): 894-904.
[2] Li, C., Liang, J. and Xiao, T.J. (2021) Long-Term Dynamical Behavior of the Wave Model with Locally Distributed Frictional and Viscoelastic Damping. Communications in Nonlinear Science and Numerical Simulation, 92, Article ID: 105472.
https://doi.org/10.1016/j.cnsns.2020.105472
[3] Liao, M., Guo, B. and Zhu, X. (2020) Bounds for Blow-Up Time to a Viscoelastic Hyperbolic Equation of Kirchhoff Type with Variable Sources. Acta Applicandae Mathematicae, 170, 1-18.
[4] Zhang, Z.Y., Liu, Z.H. and Gan, X.Y. (2013) Global Existence and General Decay for a Nonlinear Viscoelastic Equation with Nonlinear Localized Damping and Velocity-Dependent Material Density. Applicable Analysis, 92, 2021-2048.
https://doi.org/10.1080/00036811.2012.716509
[5] Mezouar, N. and Boulaaras, S. (2020) Global Existence and Decay of Solutions for a Class of Viscoelastic Kirchhoff Equation. Bulletin of the Malaysian Mathematical Sciences Society, 43, 725-755.
https://doi.org/10.1007/s40840-018-00708-2
[6] Lazo, P.P.D. (2011) Global Solution for a Quasilinear Wave Equation with Singular Memory. Applied Mathematics and Computation, 217, 7660-7668.
https://doi.org/10.1016/j.amc.2011.02.069
[7] Wang, H. and Elcrat, A.R. (1993) Boundary Control of Weakly Nonlinear Wave Equations with an Application to Galloping of Transmission Lines. Dynamics and Control, 3, 281-300.
https://doi.org/10.1007/BF01972700
[8] Sun, B. and Huang, T. (2014) Chaotic Oscillations of the Klein-Gordon Equation with Dis- tributed Energy Pumping and van der Pol Boundary Regulation and Distributed Time-Varying Coefficients. Electronic Journal of Differential Equations, 2014, 1-28.

为你推荐