J. Pruss – Moving Interfaces and Quasilinear Parabolic Evolution Equations (2016)

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Автор: J. Pruss
Название книги: Moving Interfaces and Quasilinear Parabolic Evolution Equations
Формат: PDF
Жанр: Математика
Страницы: 618
Качество: Изначально компьютерное, E-book

In this monograph, the authors develop a comprehensive approach for the mathematical analysis of a wide array of problems involving moving interfaces. It includes an in-depth study of abstract quasilinear parabolic evolution equations, elliptic and parabolic boundary value problems, transmission problems, one- and two-phase Stokes problems, and the equations of incompressible viscous one- and two-phase fluid flows. The theory of maximal regularity, an essential element, is also fully developed. The authors present a modern approach based on powerful tools in classical analysis, functional analysis, and vector-valued harmonic analysis.
The theory is applied to problems in two-phase fluid dynamics and phase transitions, one-phase generalized Newtonian fluids, nematic liquid crystal flows, Maxwell-Stefan diffusion, and a variety of geometric evolution equations. The book also includes a discussion of the underlying physical and thermodynamic principles governing the equations of fluid flows and phase transitions, and an exposition of the geometry of moving hypersurfaces.
Table of contents
Problems and Strategies
Tools from Differential Geometry
Operator Theory and Semigroups
Vector-Valued Harmonic Analysis
Quasilinear Parabolic Evolution Equations
Elliptic and Parabolic Problems
Generalized Stokes Problems
Two-Phase Stokes Problems
Local Well-Posedness and Regularity
Linear Stability of Equilibria
Qualitative Behaviour of the Semiflows
Further Parabolic Evolution Problems