带有转动惯量和强阻尼的梁方程的时间依赖吸引子
The Time-Dependent Attractor forBeam Equation with Rotational Inertia
DOI: 10.12677/PM.2023.1312371, PDF, 下载: 54  浏览: 75  国家自然科学基金支持
作者: 王 伟, 汪 璇：西北师范大学，数学与统计学院，甘肃 兰州
关键词: 梁方程；转动惯量；适定性；时间依赖吸引子；Beam Equation； Rotational Inertia； Well-Posedness； Time-Dependent Attractors
摘要: 本文讨论了带有转动惯量梁方程: ε(t)(1 +(-Δ)α)∂t2u+Δ2u-γΔ∂tu+ f(u) = g(x)，α∈[0,1)解的渐近性态，当在非线性项满足时，应用 Faedo-Galerkin 逼近方法和渐近正则估计技术，得到了解的适定性和正则性，进一步应用收缩函数方法，验证了过程的渐近紧性，最后获得了时间依赖吸引子在时间依赖空间 Htα的存在性。
Abstract: In this paper, the authors study the asymptotic behavior of the solutions to the beam equation with rotational inertia and strong damping: ε(t)(1 +(-Δ)α)∂t2u+Δ2u-γΔ∂tu+ f(u) = g(x), Whereα∈[0,1). When the growth exponent of nonlinear terms satisfies firstly, by use Faedo-Galerkin approximation method and asymptotic regular estimate technique, the well-posedness and regularity of solutions are established; secondly, the asymptotic compactness of the solution process is proved via the method of contraction function; finally, the existence of time-dependent attractor is obtained in the time-dependent space Htα.
文章引用：王伟, 汪璇. 带有转动惯量和强阻尼的梁方程的时间依赖吸引子[J]. 理论数学, 2023, 13(12): 3565-3593. https://doi.org/10.12677/PM.2023.1312371

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