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
This paper is devoted to the study of the existence of insensitizing controls for the parabolic equation with equivalued surface boundary conditions. The insensitizing problem consists in finding a control function su...This paper is devoted to the study of the existence of insensitizing controls for the parabolic equation with equivalued surface boundary conditions. The insensitizing problem consists in finding a control function such that some energy functional of the equation is locally insensitive to a perturbation of the initial data. As usual, this problem can be reduced to a partially null controllability problem for a cascade system of two parabolic equations with equivalued surface boundary conditions. Compared the problems with usual boundary conditions~ in the present case we need to derive a new global Carleman estimate, for which, in particular one needs to construct a new weight function to match the equivalued surface boundary conditions.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
Motivated by the study on the spontaneous potential well-logging, this paper deals with the homogenization of boundary conditions for a class of elliptic problems with jump interface conditions.
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Supported by National Natural Science Foundation of China (Grant Nos. 10831007 and 60974035)
文摘This paper is devoted to the study of the existence of insensitizing controls for the parabolic equation with equivalued surface boundary conditions. The insensitizing problem consists in finding a control function such that some energy functional of the equation is locally insensitive to a perturbation of the initial data. As usual, this problem can be reduced to a partially null controllability problem for a cascade system of two parabolic equations with equivalued surface boundary conditions. Compared the problems with usual boundary conditions~ in the present case we need to derive a new global Carleman estimate, for which, in particular one needs to construct a new weight function to match the equivalued surface boundary conditions.
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Motivated by the study on the spontaneous potential well-logging, this paper deals with the homogenization of boundary conditions for a class of elliptic problems with jump interface conditions.
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.
