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The Classical Stefan Problem

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The Classical Stefan Problem

The Classical Stefan Problem Book
Author : S.C. Gupta
Publisher : Elsevier
Release : 2003-10-22
ISBN : 008052916X
Language : En, Es, Fr & De

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Book Description :

This volume emphasises studies related to classical Stefan problems. The term "Stefan problem" is generally used for heat transfer problems with phase-changes such as from the liquid to the solid. Stefan problems have some characteristics that are typical of them, but certain problems arising in fields such as mathematical physics and engineering also exhibit characteristics similar to them. The term ``classical" distinguishes the formulation of these problems from their weak formulation, in which the solution need not possess classical derivatives. Under suitable assumptions, a weak solution could be as good as a classical solution. In hyperbolic Stefan problems, the characteristic features of Stefan problems are present but unlike in Stefan problems, discontinuous solutions are allowed because of the hyperbolic nature of the heat equation. The numerical solutions of inverse Stefan problems, and the analysis of direct Stefan problems are so integrated that it is difficult to discuss one without referring to the other. So no strict line of demarcation can be identified between a classical Stefan problem and other similar problems. On the other hand, including every related problem in the domain of classical Stefan problem would require several volumes for their description. A suitable compromise has to be made. The basic concepts, modelling, and analysis of the classical Stefan problems have been extensively investigated and there seems to be a need to report the results at one place. This book attempts to answer that need.

The Stefan Problem

The Stefan Problem Book
Author : A.M. Meirmanov
Publisher : Walter de Gruyter
Release : 1992-01-01
ISBN : 3110846721
Language : En, Es, Fr & De

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Book Description :

The aim of the series is to present new and important developments in pure and applied mathematics. Well established in the community over two decades, it offers a large library of mathematics including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers wishing to thoroughly study the topic. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany

The Stefan Problem

The Stefan Problem Book
Author : L. I. Rubinšteĭn
Publisher : American Mathematical Soc.
Release : 2000-01-25
ISBN : 1470428504
Language : En, Es, Fr & De

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Book Description :

Translations of Mathematical Monographs

The Classical Stefan Problem

The Classical Stefan Problem Book
Author : S. C. Gupta
Publisher : Elsevier
Release : 2017-05-01
ISBN : 9780444635815
Language : En, Es, Fr & De

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Book Description :

The Classical Stefan Problem: Basic Concepts, Modelling and Analysis, Second Edition, provides the fundamental theoretical concepts, modeling, and analysis of the physical, mathematical, thermodynamical, and metallurgical properties of classical Stefan and Stefan-like problems applied to heat transfer problems with phase-changes, such as from liquid to solid. This self-contained work reports and derives the results from tensor analysis, differential geometry, non-equilibrium thermodynamics, physics, and functional analysis. The text is enriched with many appropriate references for in-depth background reading on theorems. Each chapter begins with basic concepts, objectives, and the directions in which the subject matter has developed. This is followed by detailed reviews of published works. This updated edition is fully revised, and contains more than 150 pages of new material on quasi-analytical solutions and methods of classical Stefan and Stefan-like problems. Provides both the phenomenology and mathematics of Stefan problems Bridges physics and mathematics in a concrete and readable way Presents well-organized chapters that start with proper definitions that are followed by explanations and end with references for further reading Includes both numerical and quasi-analytical solutions and methods of classical Stefan and Stefan-like problems

The One Dimensional Heat Equation

The One Dimensional Heat Equation Book
Author : John Rozier Cannon
Publisher : Cambridge University Press
Release : 1984-12-28
ISBN : 9780521302432
Language : En, Es, Fr & De

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Book Description :

This is a version of Gevrey's classical treatise on the heat equations. Included in this volume are discussions of initial and/or boundary value problems, numerical methods, free boundary problems and parameter determination problems. The material is presented as a monograph and/or information source book. After the first six chapters of standard classical material, each chapter is written as a self-contained unit except for an occasional reference to elementary definitions, theorems and lemmas in previous chapters.

Mathematical Modeling Of Melting And Freezing Processes

Mathematical Modeling Of Melting And Freezing Processes Book
Author : V. Alexiades
Publisher : Routledge
Release : 2018-05-02
ISBN : 135143327X
Language : En, Es, Fr & De

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Book Description :

This reference book presents mathematical models of melting and solidification processes that are the key to the effective performance of latent heat thermal energy storage systems (LHTES), utilized in a wide range of heat transfer and industrial applications. This topic has spurred a growth in research into LHTES applications in energy conservation and utilization, space station power systems, and thermal protection of electronic equipment in hostile environments. Further, interest in mathematical modeling has increased with the speread of high powered computers used in most industrial and academic settings. In two sections, the book first describes modeling of phase change processes and then describes applications for LHTES. It is aimed at graduate students, researchers, and practicing engineers in heat transfer, materials processing, multiphase systems, energy conservation, metallurgy, microelectronics, and cryosurgery.

Kernel Functions and Elliptic Differential Equations in Mathematical Physics

Kernel Functions and Elliptic Differential Equations in Mathematical Physics Book
Author : Stefan Bergman,Menahem Schiffer
Publisher : Courier Corporation
Release : 2013-01-23
ISBN : 0486154653
Language : En, Es, Fr & De

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Book Description :

Covers the theory of boundary value problems in partial differential equations and discusses a portion of the theory from a unifying point of view while providing an introduction to each branch of its applications. 1953 edition.

Parabolic Equations in Biology

Parabolic Equations in Biology Book
Author : Benoît Perthame
Publisher : Springer
Release : 2015-09-09
ISBN : 331919500X
Language : En, Es, Fr & De

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Book Description :

This book presents several fundamental questions in mathematical biology such as Turing instability, pattern formation, reaction-diffusion systems, invasion waves and Fokker-Planck equations. These are classical modeling tools for mathematical biology with applications to ecology and population dynamics, the neurosciences, enzymatic reactions, chemotaxis, invasion waves etc. The book presents these aspects from a mathematical perspective, with the aim of identifying those qualitative properties of the models that are relevant for biological applications. To do so, it uncovers the mechanisms at work behind Turing instability, pattern formation and invasion waves. This involves several mathematical tools, such as stability and instability analysis, blow-up in finite time, asymptotic methods and relative entropy properties. Given the content presented, the book is well suited as a textbook for master-level coursework.

Quantum Classical Correspondence

Quantum Classical Correspondence Book
Author : A. O. Bolivar
Publisher : Springer Science & Business Media
Release : 2013-04-09
ISBN : 3662096498
Language : En, Es, Fr & De

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Book Description :

At what level of physical existence does "quantum behavior" begin? How does it develop from classical mechanics? This book addresses these questions and thereby sheds light on fundamental conceptual problems of quantum mechanics. It elucidates the problem of quantum-classical correspondence by developing a procedure for quantizing stochastic systems (e.g. Brownian systems) described by Fokker-Planck equations. The logical consistency of the scheme is then verified by taking the classical limit of the equations of motion and corresponding physical quantities. Perhaps equally important, conceptual problems concerning the relationship between classical and quantum physics are identified and discussed. Graduate students and physical scientists will find this an accessible entrée to an intriguing and thorny issue at the core of modern physics.

Classical Trade Protectionism 1815 1914

Classical Trade Protectionism 1815 1914 Book
Author : Jean-Pierre Dormois,Pedro Lains
Publisher : Routledge
Release : 2006-11-22
ISBN : 1134262965
Language : En, Es, Fr & De

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Book Description :

Including contributions from such figures as Douglas Irwin, James Foreman-Peck, Kevin O'Rourke and Max-Stefan-Schulze, this key book summarizes the recent empirical research carried out on the issue of the classical period of trade protectionism. It provides a basis for revising widely held views on the standard effects of tariffs on economic structures and progress, as well as a historical perspective on recent developments. Long-held views on modern trade policies have been challenged by the introduction of recent theoretical developments in international economics and in measurement techniques brought about in the 1960s and 70s. One question in particular has attracted attention and has contributed to the bringing to light of a number of previously ignored measurement and interpretation problems: the assessment of French and British nineteenth century trade policies. This noteworthy volume examines the theoretical and practical problems associated with the assessment and measurement of the direct impact of tariffs, prohibitions and quotas on domestic prices, output structure and competitiveness. The contributors also examine the direct and long-run consequences of protectionist measures on particular economies, utilizing evidence from in-depth investigations of trade statistics as well as ‘best practice’ statistical techniques such as effective protection, elasticity of demand and revealed comparative advantage.

Introduction to Piecewise Differentiable Equations

Introduction to Piecewise Differentiable Equations Book
Author : Stefan Scholtes
Publisher : Springer Science & Business Media
Release : 2012-08-01
ISBN : 1461443407
Language : En, Es, Fr & De

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Book Description :

​​​​​​​ This brief provides an elementary introduction to the theory of piecewise differentiable functions with an emphasis on differentiable equations. In the first chapter, two sample problems are used to motivate the study of this theory. The presentation is then developed using two basic tools for the analysis of piecewise differentiable functions: the Bouligand derivative as the nonsmooth analogue of the classical derivative concept and the theory of piecewise affine functions as the combinatorial tool for the study of this approximation function. In the end, the results are combined to develop inverse and implicit function theorems for piecewise differentiable equations. This Introduction to Piecewise Differentiable Equations will serve graduate students and researchers alike. The reader is assumed to be familiar with basic mathematical analysis and to have some familiarity with polyhedral theory.

The Classical Stefan Problem

The Classical Stefan Problem Book
Author : S. C. Gupta (Ph. D., D. Sc.),S. C. Gupta
Publisher : Jai Press
Release : 2003
ISBN : 9780444510860
Language : En, Es, Fr & De

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Book Description :

For example, the description of some phase-field models in Chapter 4 arose out of this need for a smooth transition between topics. In the mathematical formulation of Stefan problems, the curvature effects and the kinetic condition are incorporated with the help of the modified Gibbs-Thomson relation. On the basis of some thermodynamical and metallurgical considerations, the modified Gibbs-Thomson relation can be derived, as has been done in the text, but the rigorous mathematical justification comes from the fact that this relation can be obtained by taking appropriate limits of phase-field models. Because of the unacceptability of some phase-field models due their so-called thermodynamical inconsistency, some consistent models have also been described. This completes the discussion of phase-field models in the present context.-

Materials Phase Change PDE Control Estimation

Materials Phase Change PDE Control   Estimation Book
Author : Shumon Koga,Miroslav Krstic
Publisher : Springer Nature
Release : 2020-11-01
ISBN : 3030584909
Language : En, Es, Fr & De

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Book Description :

This monograph introduces breakthrough control algorithms for partial differential equation models with moving boundaries, the study of which is known as the Stefan problem. The algorithms can be used to improve the performance of various processes with phase changes, such as additive manufacturing. Using the authors' innovative design solutions, readers will also be equipped to apply estimation algorithms for real-world phase change dynamics, from polar ice to lithium-ion batteries. A historical treatment of the Stefan problem opens the book, situating readers in the larger context of the area. Following this, the chapters are organized into two parts. The first presents the design method and analysis of the boundary control and estimation algorithms. Part two then explores a number of applications, such as 3D printing via screw extrusion and laser sintering, and also discusses the experimental verifications conducted. A number of open problems and provided as well, offering readers multiple paths to explore in future research. Materials Phase Change PDE Control & Estimation is ideal for researchers and graduate students working on control and dynamical systems, and particularly those studying partial differential equations and moving boundaries. It will also appeal to industrial engineers and graduate students in engineering who are interested in this area.

One dimensional Stefan Problems

One dimensional Stefan Problems Book
Author : James M. Hill
Publisher : Longman Sc & Tech
Release : 1987
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download One dimensional Stefan Problems book written by James M. Hill, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

The Mathematics of Shock Reflection Diffraction and von Neumann s Conjectures

The Mathematics of Shock Reflection Diffraction and von Neumann s Conjectures Book
Author : Gui-Qiang G Chen,Mikhail Feldman
Publisher : Princeton University Press
Release : 2018-02-27
ISBN : 1400885434
Language : En, Es, Fr & De

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Book Description :

This book offers a survey of recent developments in the analysis of shock reflection-diffraction, a detailed presentation of original mathematical proofs of von Neumann's conjectures for potential flow, and a collection of related results and new techniques in the analysis of partial differential equations (PDEs), as well as a set of fundamental open problems for further development. Shock waves are fundamental in nature. They are governed by the Euler equations or their variants, generally in the form of nonlinear conservation laws—PDEs of divergence form. When a shock hits an obstacle, shock reflection-diffraction configurations take shape. To understand the fundamental issues involved, such as the structure and transition criteria of different configuration patterns, it is essential to establish the global existence, regularity, and structural stability of shock reflection-diffraction solutions. This involves dealing with several core difficulties in the analysis of nonlinear PDEs—mixed type, free boundaries, and corner singularities—that also arise in fundamental problems in diverse areas such as continuum mechanics, differential geometry, mathematical physics, and materials science. Presenting recently developed approaches and techniques, which will be useful for solving problems with similar difficulties, this book opens up new research opportunities.

Free Boundary Problems in Continuum Mechanics

Free Boundary Problems in Continuum Mechanics Book
Author : S.N. Antontsev,K.H. Hoffmann,A.M. Khludnev
Publisher : Birkhäuser
Release : 2013-03-07
ISBN : 3034886276
Language : En, Es, Fr & De

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Book Description :

Progress in different fields of mechanics, such as filtra tion theory, elastic-plastic problems, crystallization pro cesses, internal and surface waves, etc., is governed to a great extent by the advances in the study of free boundary problems for nonlinear partial differential equations. Free boundary problems form a scientific area which attracts attention of many specialists in mathematics and mechanics. Increasing interest in the field has given rise to the "International Conferences on Free Boundary Problems and Their Applications" which have convened, since the 1980s, in such countries as England, the United states, Italy, France and Germany. This book comprises the papers presented at the Interna tional Conference "Free Boundary Problems in Continuum Mechanics", organized by the Lavrentyev Institute of Hydrodynamics, Russian Academy of Sciences, July 15-19, 1991, Novosibirsk, Russia. The scientific committee consisted of: Co-chairmen: K.-H. Hoffmann, L.V. Ovsiannikov S. Antontsev (Russia) J. Ockendon (UK) M. Fremond (France) L. Ovsiannikov (Russia) A. Friedman (USA) S. Pokhozhaev (Russia) K.-H. Hoffmann (Germany) M. Primicerio (Italy) A. Khludnev (Russia) V. Pukhnachov (Russia) V. Monakhov (Russia) Yu. Shokin (Russia) V. Teshukov (Russia) Our thanks are due to the members of the Scientific Com mittee, all authors, and participants for contributing to the success of the Conference. We would like to express special appreciation to N. Makarenko, J. Mal'tseva and T. Savelieva, Lavrentyev Institute of Hydrodynamics, for their help in preparing this book for publication

Methods for Solving Inverse Problems in Mathematical Physics

Methods for Solving Inverse Problems in Mathematical Physics Book
Author : Global Express Ltd. Co.,Aleksey I. Prilepko,Dmitry G. Orlovsky,Igor A. Vasin
Publisher : CRC Press
Release : 2000-03-21
ISBN : 9780824719876
Language : En, Es, Fr & De

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Book Description :

Developing an approach to the question of existence, uniqueness and stability of solutions, this work presents a systematic elaboration of the theory of inverse problems for all principal types of partial differential equations. It covers up-to-date methods of linear and nonlinear analysis, the theory of differential equations in Banach spaces, applications of functional analysis, and semigroup theory.

Free Boundaries in Rock Mechanics

Free Boundaries in Rock Mechanics Book
Author : Anvarbek Meirmanov,Oleg V. Galtsev,Reshat N. Zimin
Publisher : Walter de Gruyter GmbH & Co KG
Release : 2017-09-11
ISBN : 3110545047
Language : En, Es, Fr & De

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Book Description :

This monograph is concerned with free-boundary problems of partial differential equations arising in the physical sciences and in engineering. The existence and uniqueness of solutions to the Hele-Shaw problem are derived and techniques to deal with the Muskat problem are discussed. Based on these, mathematical models for the dynamics of cracks in underground rocks and in-situ leaching are developed. Contents Introduction The Hele–Shaw problem A joint motion of two immiscible viscous fluids Mathematical models of in-situ leaching Dynamics of cracks in rocks Elements of continuum mechanics

Moving Interfaces and Quasilinear Parabolic Evolution Equations

Moving Interfaces and Quasilinear Parabolic Evolution Equations Book
Author : Jan Prüss,Gieri Simonett
Publisher : Birkhäuser
Release : 2016-07-25
ISBN : 3319276980
Language : En, Es, Fr & De

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Book Description :

In this monograph, the authors develop a comprehensive approach for the mathematical analysis of a wide array of problems involving moving interfaces. It includes an in-depth study of abstract quasilinear parabolic evolution equations, elliptic and parabolic boundary value problems, transmission problems, one- and two-phase Stokes problems, and the equations of incompressible viscous one- and two-phase fluid flows. The theory of maximal regularity, an essential element, is also fully developed. The authors present a modern approach based on powerful tools in classical analysis, functional analysis, and vector-valued harmonic analysis. The theory is applied to problems in two-phase fluid dynamics and phase transitions, one-phase generalized Newtonian fluids, nematic liquid crystal flows, Maxwell-Stefan diffusion, and a variety of geometric evolution equations. The book also includes a discussion of the underlying physical and thermodynamic principles governing the equations of fluid flows and phase transitions, and an exposition of the geometry of moving hypersurfaces.

Variational and Free Boundary Problems

Variational and Free Boundary Problems Book
Author : Avner Friedman,Joel Spruck
Publisher : Springer Science & Business Media
Release : 2012-12-06
ISBN : 1461383579
Language : En, Es, Fr & De

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Book Description :

This IMA Volume in Mathematics and its Applications VARIATIONAL AND FREE BOUNDARY PROBLEMS is based on the proceedings of a workshop which was an integral part of the 1990- 91 IMA program on "Phase Transitions and Free Boundaries. " The aim of the workshop was to highlight new methods, directions and problems in variational and free boundary theory, with a concentration on novel applications of variational methods to applied problems. We thank R. Fosdick, M. E. Gurtin, W. -M. Ni and L. A. Peletier for organizing the year-long program and, especially, J. Sprock for co-organizing the meeting and co-editing these proceedings. We also take this opportunity to thank the National Science Foundation whose financial support made the workshop possible. Avner Friedman Willard Miller, Jr. PREFACE In a free boundary one seeks to find a solution u to a partial differential equation in a domain, a part r of its boundary of which is unknown. Thus both u and r must be determined. In addition to the standard boundary conditions on the un known domain, an additional condition must be prescribed on the free boundary. A classical example is the Stefan problem of melting of ice; here the temperature sat isfies the heat equation in the water region, and yet this region itself (or rather the ice-water interface) is unknown and must be determined together with the tempera ture within the water. Some free boundary problems lend themselves to variational formulation.