Free Boundary Problems

by ; ;
Format: Hardcover
Pub. Date: 2006-11-15
Publisher(s): Birkhauser
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Summary

This book gathers a collection of 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.

Table of Contents

Preface ix
T. Aiki and T. Okazaki
One-dimensional Shape Memory Alloy Problem with Duhem Type of Hysteresis Operator
1
F. Andreu, N. Igbida, J.M. Mazón and J. Toledo
Existence and Uniqueness Results for Quasi-linear Elliptic and Parabolic Equations with Nonlinear Boundary Conditions
11
S. Antontsev and H.B. de Oliveira
Finite Time Localized Solutions of Fluid Problems with Anisotropic Dissipation
23
S. Antontsev and S. Shmarev
Parabolic Equations with Anisotropic Nonstandard Growth Conditions
33
M. Aso, M. Frémond and N. Kenmochi
Parabolic Systems with the Unknown Dependent Constraints Arising in Phase Transitions
45
A. Azevedo, J.F. Rodrigues and L. Santos
The N-membranes Problem with Neumann Type Boundary Condition
55
M. Bause and W. Merz
Modelling, Analysis and Simulation of Bioreactive Multicomponent Transport
65
G. Bellettini and R. March
Asymptotic Properties of the Nitzberg-Mumford Variational Model for Segmentation with Depth
75
M. Belloni
The infinity-Laplacian First Eigenvalue Problem
85
A. Bermúdez, M. Rodriguez-Nogueiras and C. Vázquez
Comparison of Two Algorithms to Solve the Fixed-strike Amerasian Options Pricing Problem
95
P. Biler and R. Stanczy
Nonlinear Diffusion Models for Self-gravitating Particles
107
A.C. Briozzo and D.A. Tarzia
Existence, Uniqueness and an Explicit Solution for a One-Phase Stefan Problem for a Non-classical Heat Equation
117
P. Cardaliaguet, F. Da Lio, N. Forcadel and R. Monneau
Dislocation Dynamics: a Non-local Moving Boundary
125
E. Chevalier
Bermudean Approximation of the Free Boundary Associated with an American Option
137
L. Consiglieri and J.F. Rodrigues
Steady-state Bingham Flow with Temperature Dependent Nonlocal Parameters and Friction
149
M. Eleuteri
Some P.D.E.s with Hysteresis
159
T. Fukao
Embedding Theorem for Phase Field Equation with Convection
169
G. Galiano and J. Velasco
A Dynamic Boundary Value Problem Arising in the Ecology of Mangroves
179
M. Garzon and J.A. Sethian
Wave Breaking over Sloping Beaches Using a Coupled Boundary Integral-Level Set Method
189
F. Gibou, C. Min and H. Ceniceros
Finite Difference Schemes for Incompressible Flows on Fully Adaptive Grids
199
Y. Giga, H. Kuroda and N. Yamazaki
Global Solvability of Constrained Singular Diffusion Equation Associated with Essential Variation
209
M.E. Glicksman, A. Lupulescu and M.B. Koss
Capillary Mediated Melting of Ellipsoidal Needle Crystals
219
E. Henriques and J.M. Urbano
Boundary Regularity at {t = 0} for a Singular Free Boundary Problem
231
D. Hilhorst, R. van der Hout, M. Mimura and I. Ohnishi
Fast Reaction Limits and Liesegang Bands
241
A.J. James and J. Lowengrub
Numerical Modeling of Surfactant Effects in Interfacial Fluid Dynamics
251
J. Kampen
The Value of an American Basket Call with Dividends Increases with the Basket Volatility
261
J.R. King and S.J. Franks
Mathematical Modelling of Nutrient-limited Tissue Growth
273
P. Krejci
Asymptotic Hysteresis Patterns in a Phase Separation Problem
283
C. Leone
Obstacle Problems for Monotone Operators with Measure Data
291
H. Li and X.-C. Tai
Piecewise Constant Level Set Method for Interface Problems
307
A. Muntean and M. Böhm
Dynamics of a Moving Reaction Interface in a Concrete Wall
317
J. Narski and M. Picasso
Adaptive Finite Elements with High Aspect Ratio for Dendritic Growth of a Binary Alloy Including Fluid Flow Induced by Shrinkage
327
C. Nitsch
A Free Boundary Problem for Nonlocal Damage Propagation in Diatomites
339
A. Pistoia
Concentrating Solutions for a Two-dimensional Elliptic Problem with Large Exponent in Nonlinearity
351
M. Röger
Existence of Weak Solutions for the Mullins-Sekerka Flow
361
R. Rossi
Existence and Approximation Results for General Rate-independent Problems via a Variable Time-step Discretization Scheme
369
A. Segatti
Global Attractors for the Quasistationary Phase Field Model: a Gradient Flow Approach
381
H. Shahgholian and G.S. Weiss
Aleksandrov and Kelvin Reflection and the Regularity of Free Boundaries
391
K. Shirakawa, A. Ito and A. Kadoya
Solvability for a PDE Model of Regional Economic Trend
403
B. Stinner
Surface Energies in Multi-phase Systems with Diffuse Phase Boundaries
413
M. Sussman and M. Ohta
High-order Techniques for Calculating Surface Tension Forces
425
Y. Tao and Q. Guo
Simulation of a Model of Tumors with Virus-therapy
435
X. Zhang and E. Zuazua
Hyperbolic-parabolic Coupled System Arising in Fluid-structure Interaction
445
List of Participants 457

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