# The Classical Stefan Problem: Basic Concepts, Modelling And Analysis (Volume 45) (North-Holland Series In Applied Mathematics And Mechanics, Volume 45)

SKU: DADAX0444510869

ISBN : 9780444510860

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### The Classical Stefan Problem: Basic Concepts, Modelling And Analysis (Volume 45) (North-Holland Series In Applied Mathematics And Mechanics, Volume 45)

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. Review "The book is well organized, so that, in spite of its complexity, the exposition is seemingly effortless and reading is greatly facilitated by a very judicions mixing of phemenomenology and mathematics. A book like this, bridging physics and mathematics in a concrete and readable way, was very much needed. Prof. Gupta's book fulfills that task nicely." --Antonio Fasano (Firenze) in: Zentralblatt MATH Database 1931 - 2005 From the Back Cover 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. Within the framework of the classical Stefan problem with the emphasis on the basic concepts, modelling and analysis, it tries to include some weak solutions and analytical and numerical solutions also. The main considerations behind this are the continuity and the clarity of exposition. 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

### Specification of The Classical Stefan Problem: Basic Concepts, Modelling And Analysis (Volume 45) (North-Holland Series In Applied Mathematics And Mechanics, Volume 45)

GENERAL | |
---|---|

Author | Gupta, S.C. |

Binding | Hardcover |

Language | English |

Edition | 1 |

ISBN-10 | 0444510869 |

ISBN-13 | 9780444510860 |

Publisher | JAI Press |

Publication Year | 05-11-2003 |

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