| 汪璇,田凯鸿.具有结构阻尼的Kirchhoff型波方程的时间依赖全局吸引子*[J].数学年刊A辑,2023,44(2):163~198 |
| 具有结构阻尼的Kirchhoff型波方程的时间依赖全局吸引子* |
| The Time-Dependent Global Attractors for Kirchhoff-Type Wave Equation with Structural Damping |
| Received:April 29, 2022 Revised:December 28, 2022 |
| DOI：10.16205/j.cnki.cama.2023.0013 |
| 中文关键词: Kirchhoff型波方程, 时间依赖吸引子, 结构阻尼, 正则性 |
| 英文关键词:Kirchhoff-Type wave equation, Time-Dependent global attractor,Structural damping, Regularity |
| 基金项目:国家自然科学基金(No.111961060, No.11961059, No.12061062) |
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| 中文摘要: |
| 本文讨论了具有结构阻尼的Kirchhoff型波方程:ε(t)?t2u - M(||?u||2)?u + (-?)γ?tu + f(u) = g(x), γ ∈(1/2, 1)解的适定性和长时间行为. 当非线性项f的增长指数满足2 6 p 6 3 + 2γ时,借助Faedo-Galerkin逼近方法和渐近正则估计, 得到了解的适定性和正则性. 继而利用收缩函数方法验证解过程的渐近紧性.最终证明了时间依赖全局吸引子在自然能量空间H01(?) × L2(?)中的的存在性. |
| 英文摘要: |
| In this paper, the authors study the well-posedness and the longtime dynamics of the solutions to the Kirchhoff wave equation with structural damping: ε(t)?t2u - M(||?u||2)?u + (-?)γ?tu + f(u) = g(x), γ ∈1/2, 1When the growth exponent satisfies 1 6 p 6 3 + 2γ, firstly, by use of Faedo-Galerkin approximation method and asymptotically 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 global attractor is obtained in the natural energy space H01(?) × L2(?) |
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