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研究生:呂佳孃
研究生(外文):Chia-niang Lu
論文名稱:Regularized Buckley-Leverett方程的行進波解
論文名稱(外文):Traveling Wave Solutions to the Regularized Buckley-Leverett Equation
指導教授:洪盟凱洪盟凱引用關係
指導教授(外文):John M. Hong
學位類別:碩士
校院名稱:國立中央大學
系所名稱:數學研究所
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2011
畢業學年度:99
語文別:英文
論文頁數:22
中文關鍵詞:守恆定律兩點邊界值問題Poincar´e-Bendixson 定理Stable Manifold 定理Regularized Buckley-Leverett 方程行進波dispersive方程
外文關鍵詞:Stable Manifold Theoremtraveling wavesconservation lawsdispersive equationsRegularized Buckley-Leverett equationPoincar´e-Bendixson Theoremtwo point boundary value problem
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在本文中,主要研究Regularized Buckley-Leverett 方程行進波解的存在性,這個問題可以簡化成兩點邊界值問題的微分方程。在給定邊界條件下,使得這個邊界值問題可以有三個平衡點。在特殊的邊界條件下,行進波解的存在性是可以在Poincare-Bendixson 定理和在Stable Manifold定理下的trapping region method證明出來。
In this thesis, we study the existence of traveling wave solutions to the regularized Buckley-Leverett equation. The problem can be reduced to a two point boundary value problem of some ordinary differential equation. We give the conditions of boundary data such that the two point boundary value problem has exactly three equilibria. The existence of traveling wave solutions for some special boundary data are provided by Poincar´e-Bendixson Theorem, and trapping region method for Stable Manifold Theorem.
中文摘要………………………………………………………………i
英文摘要…………………………………………………………… ii
Contents……………………………………………………………iii
1. Introduction……………………………………………………01
2. Derivation of Regularized Buckley-Leverett Equation…02
3. Equilibria of Equation for Traveling Waves……………05
4. Existence of Traveling Wave Solutions…………………10
5. References……………………………………………………21
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