Local Existence of Classical Solutions to Two Types of Regularized Buckley-Leverett Equations

• Main Authors: Yi-Ting Chen, 陳宜廷
• Other Authors: John M. Hong
• Format: Others
• Language: en_US
• Published: 2011
• Online Access: http://ndltd.ncl.edu.tw/handle/02090292070156467993

碩士 === 國立中央大學 === 數學研究所 === 99 === 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.