Free Boundary Problems

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Free Boundary Problems

Pierluigi Colli,Claudio Verdi,Augusto Visintin
Free Boundary Problems Book PDF

Author : Pierluigi Colli,Claudio Verdi,Augusto Visintin
Publisher : Birkhäuser
Page : 342 pages
File Size : 50,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034878937

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Free Boundary Problems by Pierluigi Colli,Claudio Verdi,Augusto Visintin Pdf

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.

A Geometric Approach to Free Boundary Problems

Luis A. Caffarelli,Sandro Salsa,S. Salsa
A Geometric Approach to Free Boundary Problems Book PDF

Author : Luis A. Caffarelli,Sandro Salsa,S. Salsa
Publisher : American Mathematical Soc.
Page : 282 pages
File Size : 49,9 Mb
Release : 2005
Category : Boundary value problems
ISBN : 9780821837849

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A Geometric Approach to Free Boundary Problems by Luis A. Caffarelli,Sandro Salsa,S. Salsa Pdf

We hope that the tools and ideas presented here will serve as a basis for the study of more complex phenomena and problems."--Jacket.

Optimal Stopping and Free-Boundary Problems

Goran Peskir,Albert Shiryaev
Optimal Stopping and Free Boundary Problems Book PDF

Author : Goran Peskir,Albert Shiryaev
Publisher : Springer Science & Business Media
Page : 515 pages
File Size : 49,6 Mb
Release : 2006-11-10
Category : Mathematics
ISBN : 9783764373900

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Optimal Stopping and Free-Boundary Problems by Goran Peskir,Albert Shiryaev Pdf

This book discloses a fascinating connection between optimal stopping problems in probability and free-boundary problems. It focuses on key examples and the theory of optimal stopping is exposed at its basic principles in discrete and continuous time covering martingale and Markovian methods. Methods of solution explained range from change of time, space, and measure, to more recent ones such as local time-space calculus and nonlinear integral equations. A chapter on stochastic processes makes the material more accessible. The book will appeal to those wishing to master stochastic calculus via fundamental examples. Areas of application include financial mathematics, financial engineering, and mathematical statistics.

Free Boundary Problems

Ioannis Athanasopoulos,Jose Francisco Rodrigues,George Makrakis
Free Boundary Problems Book PDF

Author : Ioannis Athanasopoulos,Jose Francisco Rodrigues,George Makrakis
Publisher : CRC Press
Page : 372 pages
File Size : 42,9 Mb
Release : 1999-06-25
Category : Mathematics
ISBN : 158488018X

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Free Boundary Problems by Ioannis Athanasopoulos,Jose Francisco Rodrigues,George Makrakis Pdf

Free boundary problems arise in an enormous number of situations in nature and technology. They hold a strategic position in pure and applied sciences and thus have been the focus of considerable research over the last three decades. Free Boundary Problems: Theory and Applications presents the work and results of experts at the forefront of current research in mathematics, material sciences, chemical engineering, biology, and physics. It contains the plenary lectures and contributed papers of the 1997 International Interdisciplinary Congress proceedings held in Crete. The main topics addressed include free boundary problems in fluid and solid mechanics, combustion, the theory of filtration, and glaciology. Contributors also discuss material science modeling, recent mathematical developments, and numerical analysis advances within their presentations of more specific topics, such as singularities of interfaces, cusp cavitation and fracture, capillary fluid dynamics of film coating, dynamics of surface growth, phase transition kinetics, and phase field models. With the implications of free boundary problems so far reaching, it becomes important for researchers from all of these fields to stay abreast of new developments. Free Boundary Problems: Theory and Applications provides the opportunity to do just that, presenting recent advances from more than 50 researchers at the frontiers of science, mathematics, and technology.

Free Boundary Problems

Darya Apushkinskaya
Free Boundary Problems Book PDF

Author : Darya Apushkinskaya
Publisher : Springer
Page : 146 pages
File Size : 50,9 Mb
Release : 2018-09-20
Category : Mathematics
ISBN : 9783319970790

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Free Boundary Problems by Darya Apushkinskaya Pdf

This book is concerned with several elliptic and parabolic obstacle-type problems with a focus on the cases where the free and fixed boundaries meet. The results presented complement those found in existing books in the subject, which mainly treat regularity properties away from the fixed boundary. The topics include optimal regularity, analysis of global solutions, tangential touch of the free and fixed boundaries, as well as Lipschitz- and $C^1$-regularity of the free boundary. Special attention is given to local versions of various monotonicity formulas. The intended audience includes research mathematicians and advanced graduate students interested in problems with free boundaries.

Free Boundary Problems in PDEs and Particle Systems

Gioia Carinci,Anna De Masi,Cristian Giardina,Errico Presutti
Free Boundary Problems in PDEs and Particle Systems Book PDF

Author : Gioia Carinci,Anna De Masi,Cristian Giardina,Errico Presutti
Publisher : Springer
Page : 110 pages
File Size : 42,9 Mb
Release : 2016-06-22
Category : Mathematics
ISBN : 9783319333700

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Free Boundary Problems in PDEs and Particle Systems by Gioia Carinci,Anna De Masi,Cristian Giardina,Errico Presutti Pdf

In this volume a theory for models of transport in the presence of a free boundary is developed.Macroscopic laws of transport are described by PDE's. When the system is open, there are several mechanisms to couple the system with the external forces. Here a class of systems where the interaction with the exterior takes place in correspondence of a free boundary is considered. Both continuous and discrete models sharing the same structure are analysed. In Part I a free boundary problem related to the Stefan Problem is worked out in all details. For this model a new notion of relaxed solution is proposed for which global existence and uniqueness is proven. It is also shown that this is the hydrodynamic limit of the empirical mass density of the associated particle system. In Part II several other models are discussed. The expectation is that the results proved for the basic model extend to these other cases.All the models discussed in this volume have an interest in problems arising in several research fields such as heat conduction, queuing theory, propagation of fire, interface dynamics, population dynamics, evolution of biological systems with selection mechanisms.In general researchers interested in the relations between PDE’s and stochastic processes can find in this volume an extension of this correspondence to modern mathematical physics.

Free Boundary Problems Involving Solids

J M Chadam,Helen Rasmussen
Free Boundary Problems Involving Solids Book PDF

Author : J M Chadam,Helen Rasmussen
Publisher : CRC Press
Page : 264 pages
File Size : 40,7 Mb
Release : 1993-02-22
Category : Mathematics
ISBN : 0582087678

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Free Boundary Problems Involving Solids by J M Chadam,Helen Rasmussen Pdf

This is the second of three volumes containing the proceedings of the International Colloquium 'Free Boundary Problems: Theory and Applications', held in Montreal from June 13 to June 22, 1990. The main theme of this volume is the concept of free boundary problems associated with solids. The first free boundary problem, the freezing of water - the Stefan problem - is the prototype of solidification problems which form the main part of this volume. The two sections treting this subject cover a large variety of topics and procedures, ranging from a theoretical mathematical treatment of solvability to numerical procedures for practical problems. Some new and interesting problems in solid mechanics are discussed in the first section while in the last section the important new subject of solid-solid-phase transition is examined.

Energy Methods for Free Boundary Problems

S.N. Antontsev,J.I. Diaz,S. Shmarev
Energy Methods for Free Boundary Problems Book PDF

Author : S.N. Antontsev,J.I. Diaz,S. Shmarev
Publisher : Springer Science & Business Media
Page : 332 pages
File Size : 55,7 Mb
Release : 2012-12-06
Category : Technology & Engineering
ISBN : 9781461200918

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Energy Methods for Free Boundary Problems by S.N. Antontsev,J.I. Diaz,S. Shmarev Pdf

For the past several decades, the study of free boundary problems has been a very active subject of research occurring in a variety of applied sciences. What these problems have in common is their formulation in terms of suitably posed initial and boundary value problems for nonlinear partial differential equations. Such problems arise, for example, in the mathematical treatment of the processes of heat conduction, filtration through porous media, flows of non-Newtonian fluids, boundary layers, chemical reactions, semiconductors, and so on. The growing interest in these problems is reflected by the series of meetings held under the title "Free Boundary Problems: Theory and Applications" (Ox ford 1974, Pavia 1979, Durham 1978, Montecatini 1981, Maubuisson 1984, Irsee 1987, Montreal 1990, Toledo 1993, Zakopane 1995, Crete 1997, Chiba 1999). From the proceedings of these meetings, we can learn about the different kinds of mathematical areas that fall within the scope of free boundary problems. It is worth mentioning that the European Science Foundation supported a vast research project on free boundary problems from 1993 until 1999. The recent creation of the specialized journal Interfaces and Free Boundaries: Modeling, Analysis and Computation gives us an idea of the vitality of the subject and its present state of development. This book is a result of collaboration among the authors over the last 15 years.

Regularity of Free Boundaries in Obstacle-Type Problems

Arshak Petrosyan,Henrik Shahgholian,Nina Nikolaevna Uralʹt︠s︡eva
Regularity of Free Boundaries in Obstacle Type Problems Book PDF

Author : Arshak Petrosyan,Henrik Shahgholian,Nina Nikolaevna Uralʹt︠s︡eva
Publisher : American Mathematical Soc.
Page : 233 pages
File Size : 55,5 Mb
Release : 2012
Category : Mathematics
ISBN : 9780821887943

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Regularity of Free Boundaries in Obstacle-Type Problems by Arshak Petrosyan,Henrik Shahgholian,Nina Nikolaevna Uralʹt︠s︡eva Pdf

The regularity theory of free boundaries flourished during the late 1970s and early 1980s and had a major impact in several areas of mathematics, mathematical physics, and industrial mathematics, as well as in applications. Since then the theory continued to evolve. Numerous new ideas, techniques, and methods have been developed, and challenging new problems in applications have arisen. The main intention of the authors of this book is to give a coherent introduction to the study of the regularity properties of free boundaries for a particular type of problems, known as obstacle-type problems. The emphasis is on the methods developed in the past two decades. The topics include optimal regularity, nondegeneracy, rescalings and blowups, classification of global solutions, several types of monotonicity formulas, Lipschitz, $C^1$, as well as higher regularity of the free boundary, structure of the singular set, touch of the free and fixed boundaries, and more. The book is based on lecture notes for the courses and mini-courses given by the authors at various locations and should be accessible to advanced graduate students and researchers in analysis and partial differential equations.

Free and Moving Boundary Problems

John Crank
Free and Moving Boundary Problems Book PDF

Author : John Crank
Publisher : Oxford University Press, USA
Page : 438 pages
File Size : 48,9 Mb
Release : 1984
Category : Mathematics
ISBN : UOM:39015047832467

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Free and Moving Boundary Problems by John Crank Pdf

Here is a wide-ranging, comprehensive account of the mathematical formulation of problems involving free boundaries as they occur in such diverse areas as hydrology, metallurgy, chemical engineering, soil science, molecular biology, materials science, and steel and glass production. Many newmethods of solution are discussed, including modern computer techniques which address multidimensional, multiphase practical problems.

Solving Free-boundary Problems with Applications in Finance

Kumar Muthuraman,Sunil Kumar
Solving Free boundary Problems with Applications in Finance Book PDF

Author : Kumar Muthuraman,Sunil Kumar
Publisher : Now Publishers Inc
Page : 94 pages
File Size : 41,8 Mb
Release : 2008
Category : Boundary value problems
ISBN : 9781601981684

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Solving Free-boundary Problems with Applications in Finance by Kumar Muthuraman,Sunil Kumar Pdf

Outlines and explains a recent computational method that solves free boundary problems by reducing them into a sequence of fixed boundary problems which are relatively easy to solve numerically.

Geometric Measure Theory and Free Boundary Problems

Guido De Philippis,Xavier Ros-Oton,Georg S. Weiss
Geometric Measure Theory and Free Boundary Problems Book PDF

Author : Guido De Philippis,Xavier Ros-Oton,Georg S. Weiss
Publisher : Springer Nature
Page : 138 pages
File Size : 47,9 Mb
Release : 2021-03-23
Category : Mathematics
ISBN : 9783030657994

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Geometric Measure Theory and Free Boundary Problems by Guido De Philippis,Xavier Ros-Oton,Georg S. Weiss Pdf

This volume covers contemporary aspects of geometric measure theory with a focus on applications to partial differential equations, free boundary problems and water waves. It is based on lectures given at the 2019 CIME summer school “Geometric Measure Theory and Applications – From Geometric Analysis to Free Boundary Problems” which took place in Cetraro, Italy, under the scientific direction of Matteo Focardi and Emanuele Spadaro. Providing a description of the structure of measures satisfying certain differential constraints, and covering regularity theory for Bernoulli type free boundary problems and water waves as well as regularity theory for the obstacle problems and the developments leading to applications to the Stefan problem, this volume will be of interest to students and researchers in mathematical analysis and its applications.

Variational Principles and Free-boundary Problems

Avner Friedman
Variational Principles and Free boundary Problems Book PDF

Author : Avner Friedman
Publisher : Courier Dover Publications
Page : 0 pages
File Size : 47,8 Mb
Release : 2010
Category : Boundary value problems
ISBN : 048647853X

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Variational Principles and Free-boundary Problems by Avner Friedman Pdf

This advanced graduate-level text examines variational methods in partial differential equations and illustrates their applications to a number of free-boundary problems. Detailed statements of the standard theory of elliptic and parabolic operators make this treatment readable for engineers, students, and nonspecialists alike. The text's first two chapters can be used for a single-semester graduate course in variational inequalities or partial differential equations. The succeeding chapters -- covering jets and cavities, variational problems with potentials, and free-boundary problems not in variational form -- are more specialized and self-contained. Readers who have mastered chapters 1 and 2 will be able to conduct research on the problems explored in subsequent chapters. Bibliographic remarks conclude each chapter, along with several problems and exercises.

Free Boundary Problems

Eduardo V. Teixeira
Free Boundary Problems Book PDF

Author : Eduardo V. Teixeira
Publisher : de Gruyter
Page : 312 pages
File Size : 41,6 Mb
Release : 2020-01-13
Category : Mathematics
ISBN : 3110574489

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Free Boundary Problems by Eduardo V. Teixeira Pdf

This book offers a comprehensive introduction to modern techniques in the study of free boundary problems of diffusive type. Applications of such methods are thoroughly explained by emblematic examples of the theory and several geometric ideas and insights are carefully discussed, making the text both accessible and appealing to a broad readership working in partial differential equations, calculus of variations, and geometric analysis.

Free Boundary Problems

Isabel Narra Figueiredo,Lisa Santos
Free Boundary Problems Book PDF

Author : Isabel Narra Figueiredo,Lisa Santos
Publisher : Springer Science & Business Media
Page : 462 pages
File Size : 50,9 Mb
Release : 2007-01-11
Category : Mathematics
ISBN : 9783764377199

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Free Boundary Problems by Isabel Narra Figueiredo,Lisa Santos Pdf

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.