EAN: 9783319276977

MOVING INTERFACES AND QUASILINEAR PARABOLIC EVO...

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.

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