| 强阻尼波动方程吸引子的正则性及其逼近 |
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| 引用本文： | 李用声,张卫国.强阻尼波动方程吸引子的正则性及其逼近[J].数学物理学报(A辑),2000,20(3):342-350. |
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| 作者姓名： | 李用声 张卫国 |
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| 作者单位： | 华中理工大学数学系!武汉430074，上海理工大学基础部!上海200093 长沙铁道学院数理力学系长沙410075 |
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| 摘 要： | 该文研究强阻尼波动方程的初边值问题．利用线性主算子在相空间中生成的解析半群的性质，证明了解的光滑效应，这个现象与弱阻尼波动方程的情形大不相同．由此作者得到了吸引子的正则性，并象自伴情形那样构造了近似惯性流形．
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| 关 键 词： | 强阻尼波动方程 解析半群 正则性 整体吸引 近似惯性流形 |
Regularity and Approximation of the Attractor for the Strongly Damped Wave Equation |
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| Li Yongsheng,Zhang Weiguo.Regularity and Approximation of the Attractor for the Strongly Damped Wave Equation[J].Acta Mathematica Scientia,2000,20(3):342-350. |
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| Authors: | Li Yongsheng Zhang Weiguo |
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| Abstract: | In this paper the authors consider the initial boundary value problem of the strongly damped wave equation. By using the analytic property of the semigroup generated by the principal operator of the equation in the phase space,they show the smoothing effect of the solution, which is much different from the case of weakly dissipative wave equations. Thus they obtain the regularity of the global attractor,and construct inertial manifolds of the equation,just as usually done in the selfadjoint cases. |
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| Keywords: | Strongly damped wave equation Analytic semigroup Regularity Global attractor Approximate inertial manifol8 |
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