1st Edition

Free Boundary Problems
Theory and Applications




ISBN 9781584880189
Published June 25, 1999 by Chapman and Hall/CRC
366 Pages

USD $195.00

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Book Description

Free boundary problems arise in an enormous number of situations in nature and technology. They hold a strategic position in pure and applied sciences and thus have been the focus of considerable research over the last three decades. Free Boundary Problems: Theory and Applications presents the work and results of experts at the forefront of current research in mathematics, material sciences, chemical engineering, biology, and physics. It contains the plenary lectures and contributed papers of the 1997 International Interdisciplinary Congress proceedings held in Crete.
The main topics addressed include free boundary problems in fluid and solid mechanics, combustion, the theory of filtration, and glaciology. Contributors also discuss material science modeling, recent mathematical developments, and numerical analysis advances within their presentations of more specific topics, such as singularities of interfaces, cusp cavitation and fracture, capillary fluid dynamics of film coating, dynamics of surface growth, phase transition kinetics, and phase field models.
With the implications of free boundary problems so far reaching, it becomes important for researchers from all of these fields to stay abreast of new developments. Free Boundary Problems: Theory and Applications provides the opportunity to do just that, presenting recent advances from more than 50 researchers at the frontiers of science, mathematics, and technology.

Table of Contents

Plenary Lectures
A Study of Free Boundary Problems of Fluid Flow in Porous Media by Mixed Methods, L. Badea, R.E. Ewing, and J. Wang
Labyrinthine Pattern Formation in Magnetic Liquids, A. Cebers, and I. Drikis
Some Two-Scale Processes Involving Parabolic Equations, A. Fasano
Level Set Methods, with an Application to Modeling the Growth of Thin Films, B. Merriman, R. Caflisch, and S. Osher
Free Boundary Problems Arising in Ecological Systems, M. Mimura
Overview of Dynamical Simulations of the Flow of Suspensions of Liquid Capsules and Drops, C. Pozrikidis
Meniscus Roll Coating: Steady Flows and Instabilities, M. Savage
Mathematical Developments of Free Boundary Problems
Instabilities, Bifurcations, and Saddle Points in some FBPs in Combustion, C.-M. Brauner, J. Hulshof, A. Lunardi, and C. Schmidt-Laine
Regularity of Solutions and Interfaces to Degenerate Parabolic Equations: The Intersection Comparison Method, V.A. Galaktionov, S. Shmarev, and J.L. Vazquez
Blow Up of Interfaces for an Inhomogeneous Aquifer, M. Guedda, D. Hilhorst, and M.A. Peletier
An Exponential Transform and Regularity of Free Boundaries in Two Dimensions, B. Gustafsson
Well-Posedness for a Phase-Field Model with Constraint, N. Kenmochi and M. Kubo
On a Structure Theorem for some Free Boundary Problems for the Heat Equation, M.K. Korten
Limit, Pointwise, Viscosity, and Classical Solutions to a Free Boundary Problem in Combustion, C. Lederman and N. Wolanski
Free Boundary Problems in Fluid Mechanics
Hysteresis Behavior of a Pointed Drop in Taylor's Four-Roller Mill, L. Antanovskii and R.H.J. Grimshaw
Mathematical Foundation of Ice Sheet and Ice Shelf Dynamics: A Physicist's View, K.H. Hutter
A Free Moving Boundary Problem for the Till Layer Below Large Ice Sheets, F. dell'Isola and K. Hutter
New Ideas about Flow Induced Cavitation of Liquids, D.D. Joseph
Topological Transitions in Liquid/Liquid Surfaces, J. Lowengrub, J. Goodman, H. Lee, E.K. Longmire, M.H. Shelley, and L. Truskinovsky
On the Mathematical Analysis of a Valley Glacier Model, J.F, Rodrigues and J.M. Urbano
On the Bernoulli Free Boundary Problem with Surface Tension, A. Wagner
Phase Change in Material Science
Alloy Solidification with Convection in the Melt, V. Alexiades
Implications of Non-Monotonic Curvature-Dependence in the Propagation Speed of an Interface, J.W. Dold
Asymptotic Analysis of a Phase-Filed Model with Memory, M. Grasselli
Models of Nucleation and Growth, A. Visintin
Computational Methods and Numerical Analysis
New Results in Numerical Conservation Laws, B. Cocburn, P.-A. Gremaud, and X. Yang
On a Degenerate System in Glaciology Giving Rise to a Free Boundary, J.I. Diaz and E. Schiavi
Singular Finite Element solutions of the Axisymmetric Extrudate-Swell Problem, G. Georgiou and A.G. Boudouvis
A Phase-Field System with Space-Dependent Relaxation Coefficient, O. Klein
Monotone Iterations for Elliptic Variational Inequalities, R. Kornhuber
Adaptive Solution of Parabolic Free Boundary Problems with Error Control, R.H. Nochetto, A. Schmidt, and C. Verdi

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