| 陈 涌.带阻尼的随机浅水波方程的随机吸引子[J].数学年刊A辑,2016,37(2):211~226 |
| 带阻尼的随机浅水波方程的随机吸引子 |
| Random Attractor of the Stochastic Damped Forced Shallow Water Equation |
| Received:December 18, 2013 Revised:September 05, 2015 |
| DOI： |
| 中文关键词: 随机浅水波方程, 随机吸引子, Bourgain空间 |
| 英文关键词:Stochastic shallow water equation, Random attractor, Bourgain space |
| 基金项目:本文受到国家自然科学基金青年基金(No.11401532, No.11501511),
浙江省自然科学基金青年基金(No.LQ14A010015, No.LQ15A010012)
和浙江理工大学科研启动基金(No.13062170-Y)的资助. |
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| 中文摘要: |
| 研究了在$H^1(\mathbb{R})$中带阻尼的随机浅水波方程的随机吸引子的存在性.
主要工具是Fourier限制范数方法以及将解分解为衰减部分与正则部分. |
| 英文摘要: |
| The existence of a random attractor is established for the stochastic damped forced shallow
water equation in $H^1(\mathbb{R})$.
The main tools are the Fourier restriction norm method and a suitable split
of the solution into a decaying part and a regular part. |
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