Regularized Buckley-Leverett方程的行進波解

Traveling Wave Solutions to the Regularized Buckley-Leverett Equation

呂佳孃(Chia-niang Lu)

指導教授 ： 洪盟凱

國立中央大學/理學院/數學系/碩士(2011年)

摘要

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。

關鍵字

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

並列摘要

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.

並列關鍵字

Stable Manifold Theorem ； traveling waves ； conservation laws ； dispersive equations ； Regularized Buckley-Leverett equation ； Poincar´e-Bendixson Theorem ； two point boundary value problem

參考文獻

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