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Moving Interfaces and Quasilinear Parabolic Evolution Equations, Paperback / softback Book

Moving Interfaces and Quasilinear Parabolic Evolution Equations Paperback / softback

Part of the Monographs in Mathematics series

Paperback / softback

Description

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 offluid flows and phase transitions, and an exposition of the geometry of moving hypersurfaces.

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