| 一类非自治Brinkman-Forchheimer方程的一致吸引子 |
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| 引用本文： | 宋雪丽,侯延仁.一类非自治Brinkman-Forchheimer方程的一致吸引子[J].数学研究及应用,2012,32(1):63-75. |
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| 作者姓名： | 宋雪丽 侯延仁 |
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| 作者单位： | 西安科技大学理学院, 陕西 西安 710054;西安交通大学理学院, 陕西 西安 710049 |
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| 基金项目： | 国家自然科学基金(Grant No.10871156). |
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| 摘 要： | This paper is concerned with the three-dimensional non-autonomous BrinkmanForchheimer equation.By Galerkin approximation method,we give the existence and uniqueness of weak solutions for non-autonomous Brinkman-Forchheimer equation.And we investigate the asymptotic behavior of the weak solution,the existence and structures of the(H,H)-uniform attractor and(H,V)-uniform attractor.Then we prove that an L 2-uniform attractor is actually an H 1-uniform attractor.
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| 关 键 词： | Galerkin approximation uniform attractor non-autonomous Brinkman-Forchheimer equation. |
| 收稿时间： | 2010/4/16 0:00:00 |
| 修稿时间： | 2010/10/11 0:00:00 |
Uniform Attractors for a Non-Autonomous Brinkman-Forchheimer Equation |
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| Xue Li SONG and Yan Ren HOU.Uniform Attractors for a Non-Autonomous Brinkman-Forchheimer Equation[J].Journal of Mathematical Research with Applications,2012,32(1):63-75. |
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| Authors: | Xue Li SONG and Yan Ren HOU |
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| Institution: | College of Science, Xi'an University of Science and Technology, Shaanxi 710054, P. R. China;College of Science, Xi'an Jiaotong University, Shaanxi 710049, P. R. China |
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| Abstract: | This paper is concerned with the three-dimensional non-autonomous Brinkman-Forchheimer equation. By Galerkin approximation method, we give the existence and uniqueness of weak solutions for non-autonomous Brinkman-Forchheimer equation. And we investigate the asymptotic behavior of the weak solution, the existence and structures of the $(H,H)$-uniform attractor and $(H,V)$-uniform attractor. Then we prove that an $L^2$-uniform attractor is actually an $H^1$-uniform attractor. |
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| Keywords: | Galerkin approximation uniform attractor non-autonomous Brinkman-Forchheimer equation |
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