在這篇論文中，我們考慮兩種類型的Regularized Buckley-Leverett方程（縮寫成RBL方程）。第一種類型的RBL方程是拋物線型的偏微分方程，而第二類的RBL方程為具有耗散和色散的偏微分方程。在第2節，我們將推導出這兩種型號的偏微分方程。在第3節，我們將使用固定點定理證明這兩個RBL方程的柯西問題的古典解的局部存在及唯一性。 In this thesis, we consider two types of regularized Buckley-Leverett equations (RBL equations for short). The first type of RBL equations are the scalar partial differential equations of parabolic type, while the second type of RBL equations are the scalar partial differential equations consist of both the dissipative and dispersive terms. In Section 2 we will derive these two models of PDEs. In Section 3 we will use the fixed point theorem to show the local existence and uniqueness of classical solutions to the Cauchy problem of these two RBL equations.
