Moving Interfaces and Quasilinear Parabolic Evolution Equations - Jan Prüss Gieri Simonett Gebunden

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 anal ysis 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.