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.

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