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Moving Interfaces and Quasilinear Parabolic Evolution Equations

Gieri Simonett, Jan Prüss

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ca. 160,49
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Springer International Publishing img Link Publisher

Naturwissenschaften, Medizin, Informatik, Technik / Analysis

Beschreibung

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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Schlagwörter

transmissions problems, partial differential equations, two-phase fluid flows, phase transitions, Navier-Stokes equations, maximal regularity, moving interfaces, vector-­valued harmonic analysis, entropy and thermodynamics, geometry of moving hypersurfaces, evolution equations