The Classical Stefan Problem: Basic Concepts, Modelling and Analysis Volume 45 (North-Holland Applied Mathematics and Mechanics") 〈45〉

Gupta, S. C.

JAI Press（2003/10発売）

• 製本 Hardcover:ハードカバー版／ページ数 404 p.
• 言語 ENG
• 商品コード 9780444510860
• DDC分類 536.2

Full 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.

Contents

1. The Stefan Problem and its Classical Formulation 2. Thermodynamical and Metallurgical Aspects of Stefan Problems 3. Extended Classical Formulations of n-phase Stefan Problems with n>1 4. Stefan Problem with Supercooling : Classical Formulation and Analysis 5. Superheating due to Volumetric Heat Sources: Formulation and Analysis 6. Steady-State and Degenerate Classical Stefan Problems 7. Elliptic and Parabolic Variational Inequalities 8. The Hyperbolic Stefan Problem 9. Inverse Stefan Problems 10. Analysis of the Classical Solutions of Stefan Problems 11. Regularity of the Weak Solutions of Some Stefan ProblemsAppendix A. Preliminaries Appendix B. Some Function Spaces and norms Appendix C. Fixed Point Theorems and Maximum Principles Appendix D. Sobolev Spaces