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Moving Interfaces and Quasilinear Parabolic Evolution Equations
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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 parapbolic 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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