Moving Interfaces and Quasilinear Parabolic Evolution Equations

Softcover Nachdruck of the original 1. Auflage 2016
ISBN: 978-3-319-80196-4
Verlag: Springer International Publishing

Buch, Englisch, Band 105, 609 Seiten, Paperback, Format (B × H): 155 mm x 235 mm, Gewicht: 9416 g

Reihe: Monographs in Mathematics

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 offluid flows and phase transitions, and an exposition of the geometry of moving hypersurfaces.

Zielgruppe

Research

Autoren/Hrsg.

Simonett, Gieri

Prüss, Jan

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik

Inhaltsverzeichnis

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.