AMS eBook CollectionsOne of the world's most respected mathematical collections, available in digital format for your library or institution
The Stefan Problem
About this Title
L. I. Rubinšteĭn. Translated by A. Solomon
Publication: Translations of Mathematical Monographs
Publication Year:
1971; Volume 27
ISBNs: 978-1-4704-2850-1 (print); 978-1-4704-4444-0 (online)
DOI: https://doi.org/10.1090/mmono/027
MathSciNet review: MR0351348
MSC: Primary 82.45
Table of Contents
Front/Back Matter
Chapters
- Introduction
- Diffusion of heat by conduction in a medium with a change of phase state
- Thermal diffusion processes in a medium with variable phase state
- Problems of the theory of filtration
- Some problems of mechanics of continuous media that reduce to problems of Stefan type
- The single-phase Stefan problem with strong nonlinearity
- The classical two-phase Stefan problem. The case of a two-phase initial state with continuous agreement of boundary and initial conditions
- The initial velocity of advance of the interphase boundary
- Solution of problems $A_1$ and $A_3$
- The double-layer Stefan problem with degeneration of one of the phases at the initial moment and a discontinuity in the boundary and initial conditions
- The spatial Stefan problem. Reduction to one dimension. The multi-phase stationary problem. A filtration analog to the Stefan problem
- The single-phase Stefan problem for a general one-dimensional equation of parabolic type. The generalized solution of the Stefan problem
- Numerical methods for the solution of the Stefan problem
- Problems