| 一类弱阻尼KdV方程的渐近光滑全局吸引子 |
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| 引用本文： | 张文彬,田立新,彭德军. 一类弱阻尼KdV方程的渐近光滑全局吸引子[J]. 江苏大学学报(自然科学版), 2005, 26(Z1): 38-41 |
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| 作者姓名： | 张文彬 田立新 彭德军 |
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| 作者单位： | 江苏大学非线性科学研究中心,江苏,镇江,212013 |
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| 基金项目： | 国家自然科学基金资助项目(10071033);江苏省自然科学基金资助项目(2000-65-31) |
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| 摘 要： | 研究带粘性项的受迫弱阻尼KdV方程,运用能量方程和正交分解相结合的方法,得到了Bourgain空间下解的正则性,结果表明在L2(R)空间中存在渐近光滑的全局吸引子.
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| 关 键 词： | 弱阻尼KdV 全局吸引子 Bourgain空间 能量方程 |
Asymptotic smoothing and global attractor of a weakly damped viscous KdV equation on real line |
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| ZHANG Wen-bin,TIAN Li-xin,PENG De-jun. Asymptotic smoothing and global attractor of a weakly damped viscous KdV equation on real line[J]. Journal of Jiangsu University:Natural Science Edition, 2005, 26(Z1): 38-41 |
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| Authors: | ZHANG Wen-bin TIAN Li-xin PENG De-jun |
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| Abstract: | The existence of the global attractor of a weakly damped,forced Korteweg-de-Vries equation in the phase space L~2(R) is proved.An optimal asymptotic smoothing effect of the equation is also shown,namely,that for forces in L~2(R),the global attractor in the phase space L~2(R) is actually a compact set in H~3(R).The energy equation method is used in conjunction with a suitable splitting of the solutions.The dispersive regulation properties of the equation in the context of Bourgain spaces are(extensively) exploited. |
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| Keywords: | weakly damped KdV global attractor Bourgain space energy equation |
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