The Classical Stefan Problem

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  • Publisher : Elsevier
  • Release : 22 October 2003
  • ISBN : 9780080529165
  • Page : 404 pages
  • Rating : 4.5/5 from 103 voters

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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.

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The Classical Stefan Problem

The Classical Stefan Problem
  • Author : S.C. Gupta
  • Publisher : Elsevier
  • Release Date : 2003-10-22
  • ISBN : 9780080529165
GET THIS BOOKThe Classical Stefan Problem

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.

The Classical Stefan Problem

The Classical Stefan Problem
  • Author : S. C. Gupta
  • Publisher : Elsevier
  • Release Date : 2017-05-01
  • ISBN : 0444635815
GET THIS BOOKThe Classical Stefan Problem

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

The Classical Stefan Problem

The Classical Stefan Problem
  • Author : S.C. Gupta
  • Publisher : Elsevier
  • Release Date : 2017-07-27
  • ISBN : 9780444635822
GET THIS BOOKThe Classical Stefan Problem

The Classical Stefan Problem: Basic Concepts, Modelling and Analysis with Quasi-Analytical Solutions and Methods, New Edition, provides the fundamental theory, concepts, modeling, and analysis of the physical, mathematical, thermodynamical, and metallurgical properties of classical Stefan and Stefan-like problems as 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, and is thoroughly enriched with many appropriate references for

The Stefan Problem

The Stefan Problem
  • Author : A.M. Meirmanov
  • Publisher : Walter de Gruyter
  • Release Date : 1992-01-01
  • ISBN : 9783110846720
GET THIS BOOKThe Stefan Problem

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

The Stefan Problem

The Stefan Problem
  • Author : L. I. Rubinšteĭn
  • Publisher : American Mathematical Soc.
  • Release Date : 2000-01-25
  • ISBN : 9781470428501
GET THIS BOOKThe Stefan Problem

Translations of Mathematical Monographs

The One-Dimensional Heat Equation

The One-Dimensional Heat Equation
  • Author : John Rozier Cannon
  • Publisher : Cambridge University Press
  • Release Date : 1984-12-28
  • ISBN : 0521302439
GET THIS BOOKThe One-Dimensional Heat Equation

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.

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  • Publisher : Courier Corporation
  • Release Date : 2013-01-23
  • ISBN : 9780486154657
GET THIS BOOKKernel Functions and Elliptic Differential Equations in Mathematical Physics

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.

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  • Publisher : Routledge
  • Release Date : 2018-05-02
  • ISBN : 9781351433280
GET THIS BOOKMathematical Modeling Of Melting And Freezing Processes

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

Variational and Free Boundary Problems

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  • Author : Avner Friedman,Joel Spruck
  • Publisher : Springer Science & Business Media
  • Release Date : 2012-12-06
  • ISBN : 9781461383574
GET THIS BOOKVariational and Free Boundary Problems

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.

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  • Author : A. O. Bolivar
  • Publisher : Springer Science & Business Media
  • Release Date : 2013-04-09
  • ISBN : 9783662096499
GET THIS BOOKQuantum-Classical Correspondence

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

Introduction to Piecewise Differentiable Equations

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  • Publisher : Springer Science & Business Media
  • Release Date : 2012-08-01
  • ISBN : 9781461443407
GET THIS BOOKIntroduction to Piecewise Differentiable Equations

​​​​​​​ 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

One-dimensional Stefan Problems

One-dimensional Stefan Problems
  • Author : James M. Hill
  • Publisher : Longman Sc & Tech
  • Release Date : 1987
  • ISBN : UOM:39015019663775
GET THIS BOOKOne-dimensional Stefan Problems

The Mathematics of Shock Reflection-Diffraction and von Neumann's Conjectures

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  • Author : Gui-Qiang G Chen,Mikhail Feldman
  • Publisher : Princeton University Press
  • Release Date : 2018-02-27
  • ISBN : 9781400885435
GET THIS BOOKThe Mathematics of Shock Reflection-Diffraction and von Neumann's Conjectures

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

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  • Publisher : Birkhäuser
  • Release Date : 2013-03-07
  • ISBN : 9783034886277
GET THIS BOOKFree Boundary Problems in Continuum Mechanics

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

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  • Publisher : Birkhäuser
  • Release Date : 2016-07-25
  • ISBN : 9783319276984
GET THIS BOOKMoving Interfaces and Quasilinear Parabolic Evolution Equations

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