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Mathematical model of spontaneous potential well-logging and its numerical solutions. (English) Zbl 1296.35001
SpringerBriefs in Mathematics. Heidelberg: Springer (ISBN 978-3-642-41424-4/pbk; 978-3-642-41425-1/ebook). vii, 67 p. (2014).
The book is devoted to the mathematical model and solution technique for the spontaneous potential well-logging. The corresponding mathematical model should be the boundary value problem of quasi-harmonic partial differential equations with inhomogeneous interface conditions. In axi-symmetric situation, at the crossing point of multiple interfaces, the compatible condition is usually violated so that it is not possible to get a solution to the boundary value problem in the sense of piecewise $$H^1$$ space. In the book the solution is sought in piecewise $$W^{1,p}$$ space $$1 < p < 2.$$ In the book, in the axi-symmetric situation it is demonstrated the well-posedness of the corresponding mathematical model and arc developed three efficient schemes of numerical solution to meet the need of practical computation.
##### MSC:
 35-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to partial differential equations 35J25 Boundary value problems for second-order elliptic equations 86A20 Potentials, prospecting 65Z05 Applications to the sciences 35Q86 PDEs in connection with geophysics
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