Some Problems On The Spontaneous Potential Well-logging

In this Ph.D.thesis,the author considers some problems on the spontaneous potential well-logging.Motivated by the study on the spontaneous potential well-logging, the author deals with the homogenization of boundary condition for a class of elliptic problems with the jump interface condition,and,presents an efficient numerical method for solving the mathematics model of the spontaneous potential well-logging.The paper is organized as follows:In Chapter 1,an introduction of the background on the spontaneous potential well-logging is given,moreover,the known conclusions and the main results of this paper are shown.In Chapter 2,the mathematical model for the spontaneous potential well-logging is given and reduced,furthermore,its corresponding variational problem is introduced.In Chapter 3,the concept of homogenization of boundary condition and the known theories are introduced,and the boundary homogenization problem in the spontaneous potential well-logging is discussed in both cases that the compatibility condition is satisfied or not.In Chapter 4,the double potential is introduced,by means of which,a numerical scheme for the spontaneous potential well-logging is suggested and some numerical examples are given.