Classical solvability for one-dimensional, free boundary, Florin, Muskat-Verigin, and Stefan problems

2000 ◽  
Vol 99 (1) ◽  
pp. 816-836 ◽  
Author(s):  
G. I. Bizhanova
Keyword(s):  
Free Boundary ◽  
One Dimensional ◽  
Stefan Problems ◽  
Classical Solvability

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.

Peeling, Slipping and Cracking—Some One-Dimensional Free-Boundary Problems in Mechanics

SIAM Review ◽  
1978 ◽  
Vol 20 (1) ◽  
pp. 31-61 ◽  
Author(s):  
R. Burridge ◽  
J. B. Keller
Keyword(s):  
Free Boundary ◽  
Free Boundary Problems ◽  
Boundary Problems ◽  
One Dimensional

Numerical methods for one-dimensional Stefan problems

2004 ◽  
Vol 20 (7) ◽  
pp. 535-545 ◽  
Author(s):  
J. Caldwell ◽  
Y. Y. Kwan
Keyword(s):  
Numerical Methods ◽  
One Dimensional ◽  
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

Internal layers in high-dimensional domains

1998 ◽  
Vol 128 (2) ◽  
pp. 359-401 ◽  
Author(s):  
Kunimochi Sakamoto
Keyword(s):  
Free Boundary ◽  
Small Parameter ◽  
Existence Of Solutions ◽  
Elliptic Partial Differential Equations ◽  
High Dimensionality ◽  
High Dimensional ◽  
Internal Layers ◽  
One Dimensional ◽  
Semilinear Elliptic ◽  
Bifurcation Phenomena

For a system of semilinear elliptic partial differential equations with a small parameter, denned on a bounded multi-dimensional smooth domain, we show the existence of solutions with internal layers. The high-dimensionality of the domain gives rise to quite interesting an outlook in the analysis, dramatically different from that in one-dimensional settings. Our analysis indicates, in a certain situation, an occurrence of an infinite series of bifurcation phenomena accumulating as the small parameter goes to zero. We also present a related free boundary problem with a possible approach to its resolution.

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