This book collects refereed lectures and communications presented at the Free Boundary Problems Conference (FBP2005). These discuss the mathematics of a broad class of models and problems involving nonlinear partial differential equations arising in physics, engineering, biology and finance. Among other topics, the talks considered free boundary problems in biomedicine, in porous media, in thermodynamic modeling, in fluid mechanics, in image processing, in financial mathematics or in computations for inter-scale problems.
One-dimensional Shape Memory Alloy Problem with Duhem Type of Hysteresis Operator.- Existence and Uniqueness Results for Quasi-linear Elliptic and Parabolic Equations with Nonlinear Boundary Conditions.- Finite Time Localized Solutions of Fluid Problems with Anisotropic Dissipation.- Parabolic Equations with Anisotropic Nonstandard Growth Conditions.- Parabolic Systems with the Unknown Dependent Constraints Arising in Phase Transitions.- The N-membranes Problem with Neumann Type Boundary Condition.- Modelling, Analysis and Simulation of Bioreactive Multicomponent Transport.- Asymptotic Properties of the Nitzberg-Mumford Variational Model for Segmentation with Depth.- The ?-Laplacian First Eigenvalue Problem.- Comparison of Two Algorithms to Solve the Fixed-strike Amerasian Options Pricing Problem.- Nonlinear Diffusion Models for Self-gravitating Particles.- Existence, Uniqueness and an Explicit Solution for a One-Phase Stefan Problem for a Non-classical Heat Equation.- Dislocation Dynamics: a Non-local Moving Boundary.- Bermudean Approximation of the Free Boundary Associated with an American Option.- Steady-state Bingham Flow with Temperature Dependent Nonlocal Parameters and Friction.- Some P.D.E.s with Hysteresis.- Embedding Theorem for Phase Field Equation with Convection.- A Dynamic Boundary Value Problem Arising in the Ecology of Mangroves.- Wave Breaking over Sloping Beaches Using a Coupled Boundary Integral-Level Set Method.- Finite Difference Schemes for Incompressible Flows on Fully Adaptive Grids.- Global Solvability of Constrained Singular Diffusion Equation Associated with Essential Variation.- Capillary Mediated Melting of Ellipsoidal Needle Crystals.- Boundary Regularity at {t = 0} for a Singular Free Boundary Problem.- Fast Reaction Limits and Liesegang Bands.- Numerical Modeling of Surfactant Effects in Interfacial Fluid Dynamics.- The Value of an American Basket Call with Dividends Increases with the Basket Volatility.- Mathematical Modelling of Nutrient-limited Tissue Growth.- Asymptotic Hysteresis Patterns in a Phase Separation Problem.- Obstacle Problems for Monotone Operators with Measure Data.- Piecewise Constant Level Set Method for Interface Problems.- Dynamics of a Moving Reaction Interface in a Concrete Wall.- Adaptive Finite Elements with High Aspect Ratio for Dendritic Growth of a Binary Alloy Including Fluid Flow Induced by Shrinkage.- A Free Boundary Problem for Nonlocal Damage Propagation in Diatomites.- Concentrating Solutions for a Two-dimensional Elliptic Problem with Large Exponent in Nonlinearity.- Existence of Weak Solutions for the Mullins-Sekerka Flow.- Existence and Approximation Results for General Rate-independent Problems via a Variable Time-step Discretization Scheme.- Global Attractors for the Quasistationary Phase Field Model: a Gradient Flow Approach.- Aleksandrov and Kelvin Reflection and the Regularity of Free Boundaries.- Solvability for a PDE Model of Regional Economic Trend.- Surface Energies in Multi-phase Systems with Diffuse Phase Boundaries.- High-order Techniques for Calculating Surface Tension Forces.- Simulation of a Model of Tumors with Virus-therapy.- Asymptotic Behavior of a Hyperbolic-parabolic Coupled System Arising in Fluid-structure Interaction.
