Coefficient Inverse Problems for Parabolic Type Equations and Their Application.

Intro -- Chapter 1.On the ill-posedness of coefficient inverse problems and the general approach to the study of them -- Chapter 2. Determining the coefficient for the lowest term of equation -- 2.1.Setting of the problem. Determination of the coefficient -- 2.2.The difference quasi-inversion problem -- 2.3.A test example -- Chapter 3. Determining of the coefficient for the leading terms of equation -- 3.1.Statement of the problem -- 3.2.The quasi-inversion problem and an estimate of stability of its solution -- 3.3.Simplification of equation of the quasi-inversion method -- 3.4.Simplification of the quasi-inversion problem -- 3.5.Finding the coefficient -- 3.6.Difference quasi-inversion problem -- 3.7.Numerical solution of the quasi-inversion problem -- 3.8.Results of solution of a test example problem -- Chapter 4. Modification of the method of determining the coefficient of the leading terms in an equation -- 4.1.Modification method -- 4.2.Defining a coefficient -- 4.3.On deriving the main integro-differential equation -- Chapter 5. Generalization of the developed algorithm for solving coefficient inversion problem -- Chapter 6. On applications of coefficient inverse problems in underground fluid dynamics -- 6.1.Determining of filtration parameters of exploited non-homogeneous oil strata -- 6.2.Determining the filtration parameters in the case of non-linear filtration -- 6.3.The quasi-inversion problem for the considered cases -- Summary -- Bibliography.

The Inverse and Ill-Posed Problems Series is a series of monographs publishing postgraduate level information on inverse and ill-posed problems for an international readership of professional scientists and researchers. The series aims to publish works which involve both theory and applications in, e.g., physics, medicine, geophysics, acoustics, electrodynamics, tomography, and ecology.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.