# Free Boundary Problems

DOI link for Free Boundary Problems

Free Boundary Problems book

# Free Boundary Problems

DOI link for Free Boundary Problems

Free Boundary Problems book

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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

part Part 1|102 pages

Plenary Lectures

chapter |11 pages

#### A Study of Free Boundary Problems of Fluid Flow in Porous Media by Mixed Methods

chapter |20 pages

#### Level Set Methods, with an Application to Modeling the Growth of Thin Films

chapter |7 pages

#### Overview of Dynamical Simulations of the Flow of Suspensions of Liquid Capsules and Drops

part Part 2|71 pages

Mathematical Developments of Free Boundary Problems

chapter |10 pages

#### Instabilities, Bifurcation and Saddle-Points in Some FBPs in Combustion

chapter |16 pages

#### Regularity of Solutions and Interfaces to Degenerate Parabolic Equations. The Intersection Comparison Method

chapter |8 pages

#### Blow-Up of Interfaces for an Inhomogeneous Aquifer

chapter |8 pages

#### An Exponential Transform and Regularity of Free Boundaries in Two Dimensions

chapter |9 pages

#### On a Structure Theorem for Some Free Boundary Problems for the Heat Equation

chapter |10 pages

#### Limit, Pointwise, Viscosity and Classical Solutions to a Free Boundary Problem in Combustion

part Part 3|77 pages

Free Boundary Problems in Fluid Mechanics

chapter |15 pages

#### Hysteresis Behaviour of a Pointed Drop in Taylor’s Four-Roller Mill

chapter |12 pages

#### Mathematical Foundation of Ice Sheet and Ice Shelf Dynamics. A Physicist’s View

chapter |6 pages

#### A Free Moving Boundary Problem for the Till Layer Below Large Ice Sheets

chapter |16 pages

#### Topological Transitions in Liquid/Liquid Interfaces

chapter |9 pages

#### On the Mathematical Analysis of a Valley Glacier Model

part Part 4|46 pages

Phase Change in Material Science

chapter |11 pages

#### Implications of Non-Monotonic Curvature-Dependence in the Propagation Speed of an Interface

part Part 5|57 pages

Computational Methods and Numerical Analysis