| 一类具有非线性kirchhoff-sine-Gordon广义方程的整体吸引子的存在性 |
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| 引用本文： | 姚华珍,张建文.一类具有非线性kirchhoff-sine-Gordon广义方程的整体吸引子的存在性[J].数学的实践与认识,2020(8):208-215. |
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| 作者姓名： | 姚华珍 张建文 |
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| 作者单位： | 太原理工大学机械与运载工程学院;太原理工大学数学学院 |
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| 基金项目： | 国家自然科学基金(11872264)。 |
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| 摘 要： | 主要目的是利用Galerkin逼近法和先验估计来证明一类具有非线性阻尼和外源项的耗散型sine-Gordon-kirchhoff方程的整体吸引子的存在性,首先通过先验估计证明系统存在唯一的整体解,再证明系统存在有界吸收集和算子半群光滑性质,最后得到系统存在整体吸引子.
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| 关 键 词： | 整体吸引子 先验估计 kirchhoff-sine-Gordon方程 非线性阻尼 |
Global Attractor for a Class of Nonlinear Generalized kirchhoff-sine-Gordon Equation |
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| YAO Hua-zhen,ZHANG Jian-wen.Global Attractor for a Class of Nonlinear Generalized kirchhoff-sine-Gordon Equation[J].Mathematics in Practice and Theory,2020(8):208-215. |
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| Authors: | YAO Hua-zhen ZHANG Jian-wen |
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| Institution: | (Taiyuan University of Technology,College of Mechanical and Vehicle Engineering,Taiyuan 030024,China;Taiyuan University of Technology,College of Mathematics,Taiyuan 030024,China) |
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| Abstract: | The aim of this paper is to prove the existence and uniqueness of the global attractor for the dissipative sine-Gordon-kirchhoff type equation with nonlinear damping and source terms on R^n,by using the Galerkin approximation method and priori estimates.Firstly,the existence and uniqueness of global solution of the system are proved by a priori estimate,and then the existence of bounded absorption set and smoothness of operator semigroup is proved.Finally,the existence of global attractor of the system is obtained. |
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| Keywords: | global attractor priori estimates kirchhoff-sine-Gordon equation nonlinear damping |
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