Moving Interfaces and Quasilinear Parabolic Evolution Equations

ISBN-13: 9783319276977 / Angielski / Twarda / 2016 / 609 str.

Jan Pruss; Gieri Simonett

Opis

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.

Recenzje

"This book is useful for readers at a variety of levels and stages. ... The book includes an extensive bibliography and bibliographical remarks throughout that serve to situate the book perfectly within its context. ... the work serves as an invaluable resource to the community." (Glen E. Wheeler, Mathematical Reviews, October, 2017)

Spis treści

Preface.- Basic Notations.- General References.- Part I Background.- 1Problems and Strategies.- 2.Tools from Differential Geometry.- Part II Abstract Theory.- 3Operator Theory and Semigroups.- 4.Vector-Valued Harmonic Analysis.- 5.Quasilinear Parabolic Evolution Equations.- Part III Linear Theory.- 6.Elliptic and Parabolic Problems.- 7.Generalized Stokes Problems.- 8.Two-Phase Stokes Problems.- Part IV Nonlinear Problems.- 9.Local Well-Posedness and Regularity.- 10.Linear Stability of Equilibria.- 11.Qualitative Behaviour of the Semiows.- 12.Further Parabolic Evolution Problems.- Biographical Comments.- Outlook and Future Challenges.- References.- List of Figures.- List of Symbols.- Subject Index.