| 退化的加权 p(x)-Laplacian 发展方程的全局吸引子 |
| Alternative Title | Global attractors for a weighted p(x)-Laplacian evolution equation with degeneracy
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| 鲁和龙 |
| Thesis Advisor | 马闪
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| 2016-06-07
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| Degree Grantor | 兰州大学
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| Place of Conferral | 兰州
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| Degree Name | 硕士
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| Keyword | 加权p(x)-Laplacian 方程
変指数
渐近先验估计
强弱连续半群
全局吸引子
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| Abstract | 本文主要考虑了有界区域上一类满足 Dirichlet 边值条件的加权 p(x)-Laplacian 发展方程解的长时间行为, 其中反应扩散系数是几乎处处有限非负可测的,在零测闭子集退化, 非线性项满足任意阶多项式增长. 首先, 用非退化方程逼近退化方程得到原方程全局弱解的存在唯一性; 其次, 得到解半群在空间 中有界吸收集的存在性, 并利用紧嵌入方法得到空间 L^2中全局吸引子的存在性; 最后, 利用渐近先验估计方法及强弱连续半群构造吸引子的理论分别得到了空间L^q(x) 和 W^{1,p(x)}_0(omega,Omega) 中全局吸引子的存在性. |
| Other Abstract | In this paper, the long-time behavior for a class of weighted p(x)-Laplacian evolution equations will be considered in a bounded domain , where the diffusion coefficient is a given nonnegative measurable and finite function a.e.in the bounded domain, the diffusion coefficient equals zero on the closed subset of the bounded domain with zero measure, the nonlinearity f satisfies a polynomial growth of arbitrary order. Firstly, the global existence and uniqueness of weak solution will be shown in variable exponent spaces using approximating degenerate problems by non-degenerate ones; Secondly, we prove the existence of absorbing sets in L^q(x) and W_0^{1,p(x)}(omega,Omega), and obtain the existence of global attractor in L^2 using the method of uniform compactness; Finally, we verify the semigroup associated with our problem is asymptotically compact in L^q(x) and W_0^{1,p(x)}(omega,Omega) using the asymptotic a priori estimate. And then the existence of global attractors in L^q(x) and W_0^{1,p(x)}(omega,Omega) are shown, respectively. |
| 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/262010/224612
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| Collection | 数学与统计学院
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Recommended Citation
GB/T 7714 |
鲁和龙. 退化的加权 p(x)-Laplacian 发展方程的全局吸引子[D]. 兰州. 兰州大学,2016.
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