DC 欄位 | 值 | 語言 |
dc.contributor | 理學院: 數學研究所 | zh: |
dc.contributor | 指導教授: 王藹農 | zh |
dc.contributor.author | 蕭煜修 | zh |
dc.contributor.author | Hsiao, Yu-Hsiu | en |
dc.creator | 蕭煜修 | zh |
dc.creator | Hsiao, Yu-Hsiu | en |
dc.date | 2014 | - |
dc.date.accessioned | 2017-03-06T05:46:19Z | - |
dc.date.accessioned | 2018-06-28T09:21:42Z | - |
dc.date.available | 2017-03-06T05:46:19Z | - |
dc.date.available | 2018-06-28T09:21:42Z | - |
dc.date.issued | 2014 | - |
dc.identifier.uri | http://ntur.lib.ntu.edu.tw//handle/246246/276904 | - |
dc.description.abstract | 在這篇論文中,我們主要討論拋物方程與雙曲方程穩態解的情形。 我們會為讀者準備充分的先備知識,由淺入深地從基本的定義開始介 紹,最終會接到我們的主題 -由橢圓方程 Lφ = f(x,φ),x ∈ Rn 出發,其 中 φ 是時間獨立的解,在某些假定的條件之下,我們將可以由穩態的解 中導出不穩定狀態的結果,為了完成我們的工作,我們主要的參考文獻為 Manoussos Grillakis, Jalal Shatah, 以及 Walter Strauss 合力完成的 [2] 與 Paschalis Karageorgis, Walter A Strauss 共同完成的 [3],基本知識的準備 我們主要參考 Lawrence C. Evans 的著作 [1] 與 Walter A. Strauss 的著作 [4]。 | zh |
dc.description.abstract | We consider the steady states solutions of parabolic and hyperbolic equa- tions such as ∂tu − ∆u = f(x, u) and ∂ttu − ∆u = f(x, u). Steady state which means a system that has numbers of properties that are unchanged in time. For instance, property p of the steady state system has zero partial derivative with respect to time : ∂p = 0. ∂t In this thesis we will give a proof about the instability results about the solutions of a general elliptic equation of the form Lφ = f (x, φ),x ∈ Rn ,where L is a linear,second-order elliptic differential operator whose coefficients are smooth and bounded. φ is the time-independent solution of Lu = f (x, u),x ∈ Rn. To complete our work, we mainly consult paper[2] and [3].Also for some basic preliminaries we consult text books[1] and [4]. | en |
dc.format.extent | 268698 bytes | - |
dc.format.mimetype | application/pdf | - |
dc.language | en | - |
dc.rights | 論文公開時間: 2020/7/22 | zh |
dc.rights | 論文使用權限: 同意無償授權 | - |
dc.subject | 非線性熱方程 | zh |
dc.subject | 非線性波方程 | zh |
dc.subject | 穩態 | zh |
dc.subject | 時間獨立 | zh |
dc.subject | Nonlinear heat equation | en |
dc.subject | Nonlinear wave equation | en |
dc.subject | Steady states | en |
dc.subject | Instability | en |
dc.title | 穩態中的不穩定狀態以偏微分方程為出發之研究與探討 | zh |
dc.title | A Survey of Instability of Steady States | en |
dc.type | thesis | en |
dc.identifier.uri.fulltext | http://ntur.lib.ntu.edu.tw/bitstream/246246/276904/1/ntu-103-R01221028-1.pdf | - |
item.cerifentitytype | Publications | - |
item.openairetype | thesis | - |
item.fulltext | with fulltext | - |
item.grantfulltext | open | - |
item.openairecristype | http://purl.org/coar/resource_type/c_46ec | - |
顯示於: | 數學系
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