
The Classical Stefan Problem: Volume 45
Basic Concepts, Modelling and Analysis
S.C. Gupta(Author)
JAI Press Inc.
Published on 22. October 2003
Book
Hardback
404 pages
978-0-444-51086-0 (ISBN)
Article exhausted; check for reprint
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.
Reviews / Votes
"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 - 2005More details
Series
Language
English
Place of publication
Oxford
United Kingdom
Publishing group
Elsevier Science & Technology
Target group
Professional and scholarly
Dimensions
Height: 229 mm
Width: 152 mm
Weight
710 gr
ISBN-13
978-0-444-51086-0 (9780444510860)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
New editions

S.C. Gupta
The Classical Stefan Problem
Basic Concepts, Modelling and Analysis with Quasi-Analytical Solutions and Methods
Book
10/2017
2nd Edition
Elsevier
€193.50
Shipment within 15-20 days
Person
Professor S.C. Gupta retired in 1997 from the Department of Mathematics, Indian Institute of Science, Bangalore, India. He holds a PhD in Solid Mechanics and a DSc in "Analytical and Numerical Solutions of Free Boundary Problems.? His areas of research are inclusion and inhomogeneity problems, thermoelasticity, numerical computations, analytical and numerical solutions of free boundary problems and Stefan problems. He has published numerous articles in reputed international journals in many areas of his research.
Author
Professor (Retired), Department of Mathematics, Indian Institute of Science, Bangalore, India
Content
1. The Stefan Problem and its Classical Formulation2. Thermodynamical and Metallurgical Aspects of Stefan Problems3. Extended Classical Formulations of n-phase Stefan Problems with n>1 4. Stefan Problem with Supercooling : Classical Formulation and Analysis5. Superheating due to Volumetric Heat Sources: Formulation and Analysis6. Steady-State and Degenerate Classical Stefan Problems7. Elliptic and Parabolic Variational Inequalities8. The Hyperbolic Stefan Problem9. Inverse Stefan Problems10. Analysis of the Classical Solutions of Stefan Problems11. Regularity of the Weak Solutions of Some Stefan Problems
Appendix A. PreliminariesAppendix B. Some Function Spaces and normsAppendix C. Fixed Point Theorems and Maximum PrinciplesAppendix D. Sobolev Spaces
Appendix A. PreliminariesAppendix B. Some Function Spaces and normsAppendix C. Fixed Point Theorems and Maximum PrinciplesAppendix D. Sobolev Spaces