| 强阻尼波方程的动力学行为 |
| Alternative Title | Dynamics for a strongly damped wave equation
|
| 杜云龙 |
| Thesis Advisor | 孙春友
|
| 2012-05-20
|
| Degree Grantor | 兰州大学
|
| Place of Conferral | 兰州
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| Degree Name | 硕士
|
| Keyword | 强阻尼波方程
渐近正则性
指数吸引子
拟单调条件
|
| Abstract | 本文研究下述定义在有界光滑区域Ω 上的强阻尼波方程
utt − Δut − Δu + f(u) = g, (x, t) ∈ Ω × R+,
(u(0), ut(0)) = (u0, v0),
u|∂Ω = 0,
解的长时间行为.对于外力项g ∈ L2(Ω)已有很好的结果, 本文主要考虑g ∈ H−1的情形.本文中, 结合稳态方程解的先验估计, 我们给出了上述强阻尼波方程解的一些新的分解方式和相应的先验估计, 最终实现在去掉拟单调性条件f′(s) > −k下依然得到解的渐近正则性和有限维指数吸引子的存在性. |
| Other Abstract | In this thesis, we consider the long-time behavior for the following strongly
damped wave equation defined on a bounded domain Ω ⊂ R3 with smooth
boundary ∂Ω:
utt − Δut − Δu + f(u) = g, (x, t) ∈ Ω × R+,
(u(0), ut(0)) = (u0, v0),
u|∂Ω = 0.
For the case g ∈ L2(Ω), the dynamics of solutions to the above equation has been the object of extensive studies. Here, we mainly consider the case g ∈ H−1.The main achievements and novelty in this thesis are two parts: the first one is that we prove some asymptotic regularity (possible optimal) for the solution
without the quasi-monotone condition f′(s) > −k; the second one is that we prove the existence of a finite-dimensional exponential attractor under the same natural assumptions. To overcome the difficulty brought by the lower regularity of forcing term, some new and refined decompositions of the solution have been devised and presented. |
| URL | 查看原文
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| Language | 中文
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| Document Type | 学位论文
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| Identifier | https://ir.lzu.edu.cn/handle/262010/224811
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| Collection | 数学与统计学院
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Recommended Citation
GB/T 7714 |
杜云龙. 强阻尼波方程的动力学行为[D]. 兰州. 兰州大学,2012.
|
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