Mathematical model of spontaneous potential well-logging and its numerical solutions. (English) Zbl 1296.35001

Li, Tatsien; Tan, Yongji; Cai, Zhijie; Chen, Wei; Wang, Jingnong

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.

Reviewer: Alla Boikova (Penza)

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