Mathematical problems and methods in resistivity well-loggings (Q1907218)

In this very extensive and complicated paper, the authors model the resistivity well-logging problem by means of a new kind of boundary value problem. The total flux boundary value problem, the variational principle for such problems and the existence and uniqueness of the solution are discussed. The procedure for solving the problem by the finite element method and some numerical results are given. The inverse problems of resistivity identification and the boundary homogenization for them are described. Generalization and applications to some other fields are presented.