Abstract
Spontaneous potential well-logging is one of the important techniques in petroleum exploitation. A spontaneous potential satisfies and elliptic equivalued surface boundary value problem with discontinuous interface conditions. In practice, the measuring electrode is so small that we can simplify the corresponding equalued 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.
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Zhijie, C. Asymptotic behavior for a class of elliptic equivalued surface boundary value problem with discontinuous interface conditions. Appl. Math. 10, 237–250 (1995). https://doi.org/10.1007/BF02662867
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DOI: https://doi.org/10.1007/BF02662867