TY  - BOOK
AU  - Prüss,Jan
AU  - Simonett,Gieri
ED  - SpringerLink (Online service)
TI  - Moving Interfaces and Quasilinear Parabolic Evolution Equations
T2  - Monographs in Mathematics,
SN  - 9783319276984
AV  - QA370-380 
U1  - 515.353 23
PY  - 2016///
CY  - Cham
PB  - Springer International Publishing, Imprint: Birkhäuser
KW  - Differential equations, partial
KW  - Mathematical physics
KW  - Functional analysis
KW  - Partial Differential Equations
KW  - Mathematical Methods in Physics
KW  - Functional Analysis
N1  - 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
N2  - 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
UR  - https://doi.org/10.1007/978-3-319-27698-4
ER  -