Free Boundary Problems: Theory and Applications

✍ Scribed by Grégoire Allaire, François Jouve, Anca-Maria Toader (auth.), Pierluigi Colli, Claudio Verdi, Augusto Visintin (eds.)

• Publisher: Birkhäuser Basel
• Year: 2004
• Tongue: English
• Leaves: 341
• Series: ISNM International Series of Numerical Mathematics 147
• Edition: 1
• Category: Library

✦ Synopsis

Many phenomena of interest for applications are represented by differential equations which are defined in a domain whose boundary is a priori unknown, and is accordingly named a "free boundary". A further quantitative condition is then provided in order to exclude indeterminacy. Free boundary problems thus encompass a broad spectrum which is represented in this state-of-the-art volume by a variety of contributions of researchers in mathematics and applied fields like physics, biology and material sciences. Special emphasis has been reserved for mathematical modelling and for the formulation of new problems.

✦ Table of Contents

Front Matter....Pages i-viii
Structural Optimization by the Level-Set Method....Pages 1-15
On a Variational Problem Arising in Image Reconstruction....Pages 17-26
Ill-Posed Hele—Shaw Flows....Pages 27-51
Finite Element Methods for Surface Diffusion....Pages 53-63
Crystal Growth and Impingement in Polymer Melts....Pages 65-74
Moving Bands and Moving Boundaries in an Hybrid Model for the Crystallization of Polymers....Pages 75-86
Upscaling of Well Singularities in the Flow Transport through Heterogeneous Porous Media....Pages 87-101
On Plasma Expansion in Vacuum....Pages 103-112
Towards the Thermodynamic Modeling of Nucleation and Growth of Liquid Droplets in Single Crystals....Pages 113-130
On the Intermediate Surface Diffusion Flow....Pages 131-138
Solid Core Revisited....Pages 139-149
Transmission-Stefan Problems Arising in Czochralski Process of Crystal Growth....Pages 151-165
Quasi-static Melting of Crystals: Experiments and Analysis....Pages 167-175
A Reduced Model for Simulating Grain Growth....Pages 177-187
On a Reaction-Diffusion System for a Population of Hunters and Farmers....Pages 189-196
The Stochastic Geometry of the Crystallization Process of Polymers....Pages 197-205
A Posteriori Error Control of Free Boundary Problems....Pages 207-223
The Total Variation Flow....Pages 225-236
A Mathematical Model for Diffusion-induced Grain Boundary Motion....Pages 237-254
Continuation of the Solution to the Chemotaxis Problem Beyond its Blow-up....Pages 255-264
Shape Deformations and Analytic Continuation in Free Boundary Problems....Pages 265-280
Error Estimates for Dissipative Evolution Problems....Pages 281-291
A Multi-mesh Finite Element Method for 3D Phase Field Simulations....Pages 293-301
Morse Description and Geometric Encoding of Digital Elevation Maps....Pages 303-312
Behavior of a Rigid Body in an Incompressible Viscous Fluid Near a Boundary....Pages 313-327
Crystal Growth, Coarsening and the Convective Cahn—Hilliard Equation....Pages 329-341
Back Matter....Pages 343-347

✦ Subjects

Partial Differential Equations; Numerical Analysis