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| 研究生： |
蘇承芳 Cheng-Fang Su |
|---|---|
| 論文名稱： |
可壓縮流中微黏性尤拉方程激波解的行為 Inner solutions for the viscous shock profiles of compressible Euler equations in a variable area duct |
| 指導教授： |
洪盟凱
John M. Hong |
| 口試委員: | |
| 學位類別： |
碩士 Master |
| 系所名稱： |
理學院 - 數學系 Department of Mathematics |
| 畢業學年度： | 97 |
| 語文別： | 英文 |
| 論文頁數： | 27 |
| 中文關鍵詞： | 守恆律 、可壓縮尤拉方程 、微黏性激波 、奇異擾動 、內部解 、外部解 |
| 外文關鍵詞： | inner solutions, conservation laws, viscous shock profiles, compressible Euler equations, outer solutions, singular perturbation |
| 相關次數： | 點閱：13 下載：0 |
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本論文中，我們考慮的是在可變面積輸送管內的可壓縮、具微黏性之尤拉方程。藉著奇異擾動下的漸近展開式技術，我們可由黏性係數的階來研究此微黏性激波的內部解行為。此外，我們亦證明出O(1)與O(ε)之內部解方程可被修正成積分微分方程的形態，利用收縮映射原理，就可建立兩點邊界值問題解之存在性與唯一性。
In this paper we consider the viscous compressible Euler equations in a variable area duct. By the technique of asymptotic expansions in singular perturbations, we study the inner solutions of the viscous shock profiles. The equations for inner solutions with respect to the power of viscous constant are derived. We show that the equations of inner solutions of O(1) and O(ε) can be modified to the scalar integro-differential equations. The existence and uniqueness of solutions for such two point boundary value problems are established by contraction mapping principle.
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