# The Classical Stefan Problem

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- Author : S.C. Gupta
- 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.

### The Classical Stefan Problem

- Author : S.C. Gupta
- Publisher : Elsevier
- Release Date : 2003-10-22
- ISBN : 9780080529165

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 Stefan Problem

- Author : A.M. Meirmanov
- Publisher : Walter de Gruyter
- Release Date : 1992-01-01
- ISBN : 9783110846720

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

- Author : L. I. Rubinšteĭn
- Publisher : American Mathematical Soc.
- Release Date : 2000-01-25
- ISBN : 9781470428501

Translations of Mathematical Monographs

### The Classical Stefan Problem

- Author : S. C. Gupta
- Publisher : Elsevier
- Release Date : 2017-05-01
- ISBN : 0444635815

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 One-Dimensional Heat Equation

- Author : John Rozier Cannon
- Publisher : Cambridge University Press
- Release Date : 1984-12-28
- ISBN : 0521302439

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.

### The Classical Stefan Problem

- Author : S. C. Gupta (Ph. D., D. Sc.),S. C. Gupta
- Publisher : Jai Press
- Release Date : 2003
- ISBN : 0444510869

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

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- Author : Benoît Perthame
- Publisher : Springer
- Release Date : 2015-09-09
- ISBN : 9783319195001

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

### Kernel Functions and Elliptic Differential Equations in Mathematical Physics

- Author : Stefan Bergman,Menahem Schiffer
- Publisher : Courier Corporation
- Release Date : 2013-01-23
- ISBN : 9780486154657

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.

### Mathematical Modeling Of Melting And Freezing Processes

- Author : V. Alexiades
- Publisher : Routledge
- Release Date : 2018-05-02
- ISBN : 9781351433273

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

### Quantum-Classical Correspondence

- Author : A. O. Bolivar
- Publisher : Springer Science & Business Media
- Release Date : 2013-04-09
- ISBN : 9783662096499

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

### Classical Trade Protectionism 1815-1914

- Author : Jean-Pierre Dormois,Pedro Lains
- Publisher : Routledge
- Release Date : 2006-11-22
- ISBN : 9781134262960

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

### Introduction to Piecewise Differentiable Equations

- Author : Stefan Scholtes
- Publisher : Springer Science & Business Media
- Release Date : 2012-08-01
- ISBN : 9781461443407

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

### Materials Phase Change PDE Control & Estimation

- Author : Shumon Koga,Miroslav Krstic
- Publisher : Springer Nature
- Release Date : 2020-11-01
- ISBN : 9783030584900

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

### Free Boundary Problems in Continuum Mechanics

- Author : S.N. Antontsev,K.H. Hoffmann,A.M. Khludnev
- Publisher : Birkhäuser
- Release Date : 2013-03-07
- ISBN : 9783034886277

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

### Moving Interfaces and Quasilinear Parabolic Evolution Equations

- Author : Jan Prüss,Gieri Simonett
- Publisher : Birkhäuser
- Release Date : 2016-07-25
- ISBN : 9783319276984

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