Free Boundary Problems: Theory and Applications, 1st Edition (Paperback) book cover

Free Boundary Problems

Theory and Applications, 1st Edition

By Ioannis Athanasopoulos, Jose Francisco Rodrigues, George Makrakis

Chapman and Hall/CRC

368 pages

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Paperback: 9781584880189
pub: 1999-06-25
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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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