This book collects refereed articles containing original results reporting the recent contributions of the lectures and communications presented at the Free Boundary Problems Conference that took place at the University of Coimbra, Portugal, from June 7 to 12, 2005 (FBP2005). They deal with the mathematics of a broad class of models and problems involving nonlinear partial differential equations arising in physics, engineering, biology and finance. Among the main 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.
Author(s): Toyohiko Aiki, Takanobu Okazaki (auth.), Isabel Narra Figueiredo, José Francisco Rodrigues, Lisa Santos (eds.)
Series: International Series of Numerical Mathematics 154
Edition: 1
Publisher: Birkhäuser Basel
Year: 2007
Language: English
Pages: 462
City: Basel; Boston
Tags: Numerical Analysis; Partial Differential Equations
Front Matter....Pages i-x
One-dimensional Shape Memory Alloy Problem with Duhem Type of Hysteresis Operator....Pages 1-9
Existence and Uniqueness Results for Quasi-linear Elliptic and Parabolic Equations with Nonlinear Boundary Conditions....Pages 11-21
Finite Time Localized Solutions of Fluid Problems with Anisotropic Dissipation....Pages 23-32
Parabolic Equations with Anisotropic Nonstandard Growth Conditions....Pages 33-44
Parabolic Systems with the Unknown Dependent Constraints Arising in Phase Transitions....Pages 45-54
The N -membranes Problem with Neumann Type Boundary Condition....Pages 55-64
Modelling, Analysis and Simulation of Bioreactive Multicomponent Transport....Pages 65-74
Asymptotic Properties of the Nitzberg-Mumford Variational Model for Segmentation with Depth....Pages 75-84
The ∞-Laplacian First Eigenvalue Problem....Pages 85-94
Comparison of Two Algorithms to Solve the Fixed-strike Amerasian Options Pricing Problem....Pages 95-106
Nonlinear Diffusion Models for Self-gravitating Particles....Pages 107-116
Existence, Uniqueness and an Explicit Solution for a One-Phase Stefan Problem for a Non-classical Heat Equation....Pages 117-124
Dislocation Dynamics: a Non-local Moving Boundary....Pages 125-135
Bermudean Approximation of the Free Boundary Associated with an American Option....Pages 137-147
Steady-state Bingham Flow with Temperature Dependent Nonlocal Parameters and Friction....Pages 149-157
Some P.D.E.s with Hysteresis....Pages 159-168
Embedding Theorem for Phase Field Equation with Convection....Pages 169-178
A Dynamic Boundary Value Problem Arising in the Ecology of Mangroves....Pages 179-188
Wave Breaking over Sloping Beaches Using a Coupled Boundary Integral-Level Set Method....Pages 189-198
Finite Difference Schemes for Incompressible Flows on Fully Adaptive Grids....Pages 199-208
Global Solvability of Constrained Singular Diffusion Equation Associated with Essential Variation....Pages 209-218
Capillary Mediated Melting of Ellipsoidal Needle Crystals....Pages 219-230
Boundary Regularity at { t = 0} for a Singular Free Boundary Problem....Pages 231-240
Fast Reaction Limits and Liesegang Bands....Pages 241-250
Numerical Modeling of Surfactant Effects in Interfacial Fluid Dynamics....Pages 251-261
The Value of an American Basket Call with Dividends Increases with the Basket Volatility....Pages 261-272
Mathematical Modelling of Nutrient-limited Tissue Growth....Pages 273-282
Asymptotic Hysteresis Patterns in a Phase Separation Problem....Pages 283-290
Obstacle Problems for Monotone Operators with Measure Data....Pages 291-305
Piecewise Constant Level Set Method for Interface Problems....Pages 307-316
Dynamics of a Moving Reaction Interface in a Concrete Wall....Pages 317-326
Adaptive Finite Elements with High Aspect Ratio for Dendritic Growth of a Binary Alloy Including Fluid Flow Induced by Shrinkage....Pages 327-337
A Free Boundary Problem for Nonlocal Damage Propagation in Diatomites....Pages 339-349
Concentrating Solutions for a Two-dimensional Elliptic Problem with Large Exponent in Nonlinearity....Pages 351-360
Existence of Weak Solutions for the Mullins-Sekerka Flow....Pages 361-368
Existence and Approximation Results for General Rate-independent Problems via a Variable Time-step Discretization Scheme....Pages 369-380
Global Attractors for the Quasistationary Phase Field Model: a Gradient Flow Approach....Pages 381-390
Aleksandrov and Kelvin Reflection and the Regularity of Free Boundaries....Pages 391-401
Solvability for a PDE Model of Regional Economic Trend....Pages 403-412
Surface Energies in Multi-phase Systems with Diffuse Phase Boundaries....Pages 413-423
High-order Techniques for Calculating Surface Tension Forces....Pages 425-434
Simulation of a Model of Tumors with Virus-therapy....Pages 435-444
Asymptotic Behavior of a Hyperbolic-parabolic Coupled System Arising in Fluid-structure Interaction....Pages 445-455
Back Matter....Pages 457-460
