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Viser: Moving Interfaces and Quasilinear Parabolic Evolution Equations
Moving Interfaces and Quasilinear Parabolic Evolution Equations Vital Source e-bog
Jan Prüss og Gieri Simonett
(2016)
Moving Interfaces and Quasilinear Parabolic Evolution Equations
Jan Prüss og Gieri Simonett
(2016)
Sprog: Engelsk
om ca. 10 hverdage
Detaljer om varen
- Vital Source searchable e-book (Fixed pages)
- Udgiver: Springer Nature (Juli 2016)
- Forfattere: Jan Prüss og Gieri Simonett
- ISBN: 9783319276984
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Detaljer om varen
- 1. Udgave
- Hardback: 603 sider
- Udgiver: Springer International Publishing AG (August 2016)
- Forfattere: Jan Prüss og Gieri Simonett
- ISBN: 9783319276977
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.
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.