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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.
List of contents
Structural Optimization by the Level-Set Method.- On a Variational Problem Arising in Image Reconstruction.- Ill-Posed Hele¡ªShaw Flows.- Finite Element Methods for Surface Diffusion.- Crystal Growth and Impingement in Polymer Melts.- Moving Bands and Moving Boundaries in an Hybrid Modelfor the Crystallization of Polymers.- Upscaling of Well Singularities in the Flow Transportthrough Heterogeneous Porous Media.- On plasma expansion in vacuum.- Towards the thermodynamic modeling of nucleation and growthof liquid droplets in single crystals.- On the Intermediate Surface Diffusion Flow.- Solid Core Revisited.- Transmission-Stefan Problems Arising in Czochralski Processof Crystal Growth.- Quasi-static Melting of Crystals: Experiments and Analysis.- A reduced model for simulating grain growth.- On a Reaction-Diffusion System for a Population of Huntersand Farmers.- The Stochastic Geometry of the Crystallization Process of Polymers.- A Posteriori Error Control of Free Boundary Problems.- The Total Variation Flow.- A Mathematical Model for Diffusion-induced Grain Boundary Motion.- Continuation of the Solution to the Chemotaxis ProblemBeyond its Blow-up.- Shape Deformations and Analytic Continuation inFree Boundary Problems.- Error Estimates for Dissipative Evolution Problems.- A Multi-mesh Finite Element Method for 3D Phase Field Simulations.- Morse Description and Geometric Encoding of Digital Elevation Maps.- Behavior of a Rigid Body in an Incompressible Viscous FluidNear a Boundary.- Crystal Growth, Coarsening and the ConvectiveCahn-Hilliard Equation.- List of Participants.
Summary
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.
