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Moving Interfaces and Quasilinear Parabolic Evolution Equations (Hardcover, 1st ed. 2016)
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Moving Interfaces and Quasilinear Parabolic Evolution Equations (Hardcover, 1st ed. 2016)
Series: Monographs in Mathematics, 105
Expected to ship within 12 - 17 working days
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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 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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