| 强耗散KDV型方程的指数吸引子 |
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| 引用本文： | 韩灵娟,马巧珍.强耗散KDV型方程的指数吸引子[J].数学研究及应用,2010,30(6):1117-1124. |
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| 作者姓名： | 韩灵娟 马巧珍 |
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| 作者单位： | 北京科技大学应用科学学院数力系, 北京 100083 |
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| 基金项目： | 国家自然科学基金(Grant Nos.10726064; 10901018);北京科技大学冶金工程研究院理论研究基金资助. |
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| 摘 要： | In this paper,we consider the strong dissipative KDV type equation on an unbounded domain R1.By applying the theory of decomposing operator and the method of constructing some compact operator in weighted space,the existence of exponential attractor in phase space H2（R1） is obtained.
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| 关 键 词： | unbounded domain KDV type equation exponential attractor. |
| 收稿时间： | 2008/10/21 0:00:00 |
| 修稿时间： | 2009/5/16 0:00:00 |
Exponential Attractor of Strong Dissipative KDV Type Equation |
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| Ling Juan HAN and Qiao Zhen MA.Exponential Attractor of Strong Dissipative KDV Type Equation[J].Journal of Mathematical Research with Applications,2010,30(6):1117-1124. |
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| Authors: | Ling Juan HAN and Qiao Zhen MA |
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| Institution: | Department of Mathematics and Mechanics, School of Applied Science, University of Science and Technology Beijing, Beijing 100083, P. R. China |
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| Abstract: | In this paper we consider the Schr\"{o}dinger operator $-\Delta_{G}+W$ on the nilpotent Lie group $G$ where the nonnegative potential $W$ belongs to the reverse H\"{o}lder class $B_{q_{_1}}$ for some $q_{_1}\geq \frac{D}{2}$ and $D$ is the dimension at infinity of $G$. The weighted $L^p-L^q$ estimates for the operators $W^\alpha(-\Delta_{G}+W)^{-\beta}$ and $W^\alpha\nabla_{G}(-\Delta_{G}+W)^{-\beta}$ are obtained. |
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| Keywords: | nilpotent Lie group Schr\"{o}dinger operators reverse H\"{o}lder class |
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