scholarly journals Semi-waves with $\Lambda $-shaped free boundary for nonlinear Stefan problems: Existence

2021 ◽  
pp. 1
Author(s):  
Yihong Du ◽  
Changfeng Gui ◽  
Kelei Wang ◽  
Maolin Zhou
Keyword(s):  
Free Boundary ◽  
Stefan Problems

scholarly journals Deep learning of free boundary and Stefan problems

2020 ◽  
pp. 109914
Author(s):  
Sifan Wang ◽  
Paris Perdikaris
Keyword(s):  
Deep Learning ◽  
Free Boundary ◽  
Stefan Problems

Stefan problems with kinetic conditions at the free boundary

1993 ◽  
Vol 8 (1) ◽  
pp. 32-44 ◽  
Author(s):  
Ling Jun
Keyword(s):  
Free Boundary ◽  
Stefan Problems

Macroscopic models for melting derived from averaging microscopic Stefan problems I: Simple geometries with kinetic undercooling or surface tension

2000 ◽  
Vol 11 (2) ◽  
pp. 153-169 ◽  
Author(s):  
A. A. LACEY ◽  
L. A. HERRAIZ
Keyword(s):  
Free Boundary ◽  
Multiple Scales ◽  
Two Dimensions ◽  
Macroscopic Model ◽  
Mushy Region ◽  
Free Boundaries ◽  
Two Phase ◽  
Macroscopic Models ◽  
Stefan Problems ◽  
Kinetic Undercooling

A mushy region is assumed to consist of a fine mixture of two distinct phases separated by free boundaries. For simplicity, the fine structure is here taken to be periodic, first in one dimension, and then a lattice of squares in two dimensions. A method of multiple scales is employed, with a classical free-boundary problem being used to model the evolution of the two-phase microstructure. Then a macroscopic model for the mush is obtained by an averaging procedure. The free-boundary temperature is taken to vary according to Gibbs–Thomson and/or kinetic-undercooling effects.

scholarly journals The Hele-Shaw problem as a ‘‘Mesa” limit of Stefan problems: Existence, uniqueness, and regularity of the free boundary

2008 ◽  
Vol 361 (03) ◽  
pp. 1241-1268 ◽  
Author(s):  
Ivan A. Blank ◽  
Marianne K. Korten ◽  
Charles N. Moore
Keyword(s):  
Free Boundary ◽  
Stefan Problems

A Four-Step Fixed-Grid Method for 1D Stefan Problems

2010 ◽  
Vol 132 (11) ◽  
Author(s):  
M. Tadi
Keyword(s):  
Free Boundary ◽  
Moving Boundary ◽  
Free Boundary Problems ◽  
Grid Method ◽  
Moving Boundary Problems ◽  
Boundary Problems ◽  
One Dimensional ◽  
Nonlinear Part ◽  
Stefan Problems ◽  
Fixed Grid

This note is concerned with a fixed-grid finite difference method for the solution of one-dimensional free boundary problems. The method solves for the field variables and the location of the boundary in separate steps. As a result of this decoupling, the nonlinear part of the algorithm involves only a scalar unknown, which is the location of the moving boundary. A number of examples are used to study the applicability of the method. The method is particularly useful for moving boundary problems with various conditions at the front.

scholarly journals One dimensional Stefan problems with nonmonotone free boundary

1968 ◽  
Vol 133 (1) ◽  
pp. 89-89 ◽  
Author(s):  
Avner Friedman
Keyword(s):  
Free Boundary ◽  
One Dimensional ◽  
Stefan Problems

Estimates of the Location of a Free Boundary for the Obstacle and Stefan Problems Obtained by Means of Some Energy Methods

2008 ◽  
Vol 15 (3) ◽  
pp. 475-484
Author(s):  
Jesús Ildefonso Díaz
Keyword(s):  
Free Boundary ◽  
Stefan Problem ◽  
Obstacle Problem ◽  
Energy Methods ◽  
Stefan Problems ◽  
Unilateral Problems

Abstract In this paper we use some energy methods to study the location (and formation) of a free boundary arising in some unilateral problems, for instance, in the obstacle problem and the Stefan problem.

A Schur complement formulation for solving free-boundary, Stefan problems of phase change

2010 ◽  
Vol 229 (20) ◽  
pp. 7942-7955 ◽  
Author(s):  
Lisa Lun ◽  
Andrew Yeckel ◽  
Jeffrey J. Derby
Keyword(s):  
Free Boundary ◽  
Phase Change ◽  
Schur Complement ◽  
Stefan Problems
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