Free Boundary Problems
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Free Boundary Problems
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Author : Darya Apushkinskaya
language : en
Publisher: Springer
Release Date : 2018-09-20
Free Boundary Problems written by Darya Apushkinskaya and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-20 with Mathematics categories.
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
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Author : Pierluigi Colli
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Free Boundary Problems written by Pierluigi Colli and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
Free Boundary Problems In Pdes And Particle Systems
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Author : Gioia Carinci
language : en
Publisher: Springer
Release Date : 2016-06-22
Free Boundary Problems In Pdes And Particle Systems written by Gioia Carinci and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-22 with Mathematics categories.
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.
Optimal Stopping And Free Boundary Problems
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Author : Goran Peskir
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-11-10
Optimal Stopping And Free Boundary Problems written by Goran Peskir and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-10 with Mathematics categories.
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.
A Geometric Approach To Free Boundary Problems
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Author : Luis A. Caffarelli
language : en
Publisher: American Mathematical Soc.
Release Date : 2005
A Geometric Approach To Free Boundary Problems written by Luis A. Caffarelli and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.
We hope that the tools and ideas presented here will serve as a basis for the study of more complex phenomena and problems."--Jacket.
Free Boundary Problems
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Author : Ioannis Athanasopoulos
language : en
Publisher: CRC Press
Release Date : 1999-06-25
Free Boundary Problems written by Ioannis Athanasopoulos and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-06-25 with Mathematics categories.
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.
Geometric Measure Theory And Free Boundary Problems
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Author : Guido De Philippis
language : en
Publisher: Springer Nature
Release Date : 2021-03-23
Geometric Measure Theory And Free Boundary Problems written by Guido De Philippis and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-23 with Mathematics categories.
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.
Free Boundary Problems
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Author : A. Bossavit
language : en
Publisher:
Release Date : 1985
Free Boundary Problems written by A. Bossavit and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with Mathematics categories.
Energy Methods For Free Boundary Problems
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Author : S.N. Antontsev
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Energy Methods For Free Boundary Problems written by S.N. Antontsev and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Technology & Engineering categories.
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.