具有奇异振荡外力的记忆型粘弹性发展方程一致吸引子的上半连续性
Upper Semicontinuity of Uniform Attractors for Memory Viscoelastic Evolution Equation with Singularly Oscillating External Forces
DOI: 10.12677/PM.2023.1312354, PDF,    国家自然科学基金支持
作者: 刘文婷：西北师范大学数学与统计学院，甘肃 兰州
关键词: 奇异振荡；弱阻尼；记忆核；一致吸引子；上半连续性；Singular Oscillations； Weak Damping； Memory Kernel； Uniform Attractors； Upper Semicontinuity
摘要: 本文主要研究了具有奇异振荡外力项和弱阻尼项的记忆型粘弹性发展方程。首先证明了在外力项和记忆核满足恰当条件时方程一致吸引子 Aε在空间H = H01(Ω)×H01(Ω)×M中的一致有界性, 进而证明了当ε→0+ 时一致吸引子的上半连续性。
Abstract: This paper is concerned with the development of memory viscoelastic equation with singularly oscillating external force terms and weak damping terms. First, we prove the consistent boundedness of the uniform attractor A" of the equation in H = H01(Ω)×H01(Ω)×M when the external force term and the memory kernel satisfy the appropriate conditions, and then the upper semicontinuity of the uniform attractor when ε→0+ is achieved.
文章引用：刘文婷. 具有奇异振荡外力的记忆型粘弹性发展方程一致吸引子的上半连续性[J]. 理论数学, 2023, 13(12): 3412-3425. https://doi.org/10.12677/PM.2023.1312354

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