带有记忆项的Kirchhoff型波方程的时间依赖全局吸引子

Time-Dependent Global Attractor for Kirchhoff-Type Wave Equations with Memory Terms

摘要

考虑一类含记忆项、非局部强阻尼及非线性扰动的 Kirchhoff 型波方程的时间依赖全局吸引子的存在性问题。首先，给出该问题解的适定性结果；其次，利用能量估计得到该动力系统在相应解空间中拉回吸收集的存在性；最后，利用收缩函数方法证明其过程的渐近性质，从而确定时间依赖全局吸引子的存在性。

Abstract

We considered the existence of time-dependent global attractors for a class of Kirchhoff-type wave equations with memory terms,nonlocal strong damping,and nonlinear perturbations．Firstly, we gave the well-posedness result of the solution to the problem．Secondly, we obtained the existence of a pullback absorbing set for the dynamical system in the corresponding solution space by using energy estimates．Finally, we proved the asymptotic properties of its process by using the method of contraction functions, thereby the existence of the time-dependent global attractor was established.

关键词

Kirchhoff 型波方程 / 记忆项 / 非局部强阻尼 / 收缩函数 / 时间依赖全局吸引子

Key words

Kirchhoff-type wave equation / memory term / nonlocal strong damping / contraction function / time-dependent global attractor

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基金资助

国家自然科学基金(11701230)

国家自然科学基金(12026431)

国家自然科学基金(12442050)

江苏高校＂青蓝工程＂和中吴创新团队项目