| 非线性Sobolev-Galpern方程的有限维整体吸引子 |
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| 引用本文： | 尚亚东,房少梅.非线性Sobolev-Galpern方程的有限维整体吸引子[J].应用数学,2003,16(4):122-129. |
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| 作者姓名： | 尚亚东 房少梅 |
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| 作者单位： | 1. 广州大学数学系,广东,广州,510405
2. 韶关大学数学系,广东,韶关,512005 |
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| 基金项目： | SupportedbyNNSFofChina(10 2 710 34 ) |
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| 摘 要： | 本文研究非线性Sobolev-Galpern方程解的渐近性态．首先证明了该方程在H^2(Ω)∩H0^1(Ω)中整体弱吸引子的存在性，然后利用一个能量方程证明了整体弱吸引子实际上是整体强吸引子，建立了整体吸引子的有限维性．
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| 关 键 词： | 非线性Sobolev-Galpern方程 整体吸引子 解 渐近性 能量方程 弱收敛性 有限维性 初边值问题 |
Finite Dimensional Global Attractors for Nonlinear Sobolev-Galpern Equations |
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| SHANG Yadong ,FANG Shaomei.Finite Dimensional Global Attractors for Nonlinear Sobolev-Galpern Equations[J].Mathematica Applicata,2003,16(4):122-129. |
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| Authors: | SHANG Yadong FANG Shaomei |
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| Institution: | SHANG Yadong 1,FANG Shaomei 2 |
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| Abstract: | In this paper, we study the asymptotic behavior of solutions for the nonlinear Sobolev-Galpern equations. We first show the existence of the global weak attractor in H2 (Ω) ∩ H10 (Ω) forthe equations. And then by an energy equation we prove that the global weak attractor is actually theglobal strong attractor. The finite dimensionality of the global attractor is also established. |
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| Keywords: | Nonlinear SobolevGalpern equations Asymptotic behavio r Global attractor Energy equation Weak continuity |
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