Spontaneous potential well-logging is one of the important techniques in petroleum exploitation. A spontaneous potential satisfies an elliptic equivalued surface boundary value problem with discontinuous interface con...Spontaneous potential well-logging is one of the important techniques in petroleum exploitation. A spontaneous potential satisfies an elliptic equivalued surface boundary value problem with discontinuous interface conditions. In practice, the measuring electrode is so small that we can simplify the corresponding equivalued surface to a point. In this paper, we give a positive answer to this approximation process:when the equivalued surface shrinks to a point, the solution of the original equivalued surface boundary value problem converges to the solution of the corresponding limit boundary value problem.展开更多
Abstract. In this paper, we discuss the limit behaviour of solutious to equivalued surfaceboundary value problem for parabolic equations when the equivalued surface boundaryshrinks to a point and the space dimension o...Abstract. In this paper, we discuss the limit behaviour of solutious to equivalued surfaceboundary value problem for parabolic equations when the equivalued surface boundaryshrinks to a point and the space dimension of the domain is two or more.展开更多
In petroleum exploitation, the main aim of resistivity well-logging is to determine the resistivity of the layers by measuring the potential on the electrodes. This mathematical problem can be described as an inverse ...In petroleum exploitation, the main aim of resistivity well-logging is to determine the resistivity of the layers by measuring the potential on the electrodes. This mathematical problem can be described as an inverse problem for the elliptic equivalued surface boundary value problem. In this paper, the author gets the expression of the derivative functions of the potential on the electrodes with respect to the resistivity of the layers. This allows us to solve the identification problem of the resistivity of the layers.展开更多
文摘Spontaneous potential well-logging is one of the important techniques in petroleum exploitation. A spontaneous potential satisfies an elliptic equivalued surface boundary value problem with discontinuous interface conditions. In practice, the measuring electrode is so small that we can simplify the corresponding equivalued surface to a point. In this paper, we give a positive answer to this approximation process:when the equivalued surface shrinks to a point, the solution of the original equivalued surface boundary value problem converges to the solution of the corresponding limit boundary value problem.
基金NSF of Shandong Province (No.Y98A09012, No. Q99A05.)
文摘Abstract. In this paper, we discuss the limit behaviour of solutious to equivalued surfaceboundary value problem for parabolic equations when the equivalued surface boundaryshrinks to a point and the space dimension of the domain is two or more.
文摘In petroleum exploitation, the main aim of resistivity well-logging is to determine the resistivity of the layers by measuring the potential on the electrodes. This mathematical problem can be described as an inverse problem for the elliptic equivalued surface boundary value problem. In this paper, the author gets the expression of the derivative functions of the potential on the electrodes with respect to the resistivity of the layers. This allows us to solve the identification problem of the resistivity of the layers.
