scholarly journals Variational methods in a mixed problem of thermal equilibrium with a free boundary

1985 ◽  
pp. 77-92
Author(s):  
B. V. Bazaliĭ ◽  
V. Yu. Shelepov
Keyword(s):  
Free Boundary ◽  
Variational Methods ◽  
Mixed Problem ◽  
Thermal Equilibrium

Liquid drops suspended by soap films. II. Simplified model

1984 ◽  
Vol 394 (1806) ◽  
pp. 33-45 ◽  
Keyword(s):  
Free Boundary ◽  
Variational Methods ◽  
Stable Equilibrium ◽  
Existence Of Solutions ◽  
Mathematical Problem ◽  
Simplified Model ◽  
Uniqueness Of Solutions ◽  
Liquid Drops ◽  
Confined Plasmas ◽  
Made In

The model consists in taking linearized approximations to the curvatures of the upper and lower surfaces, but the problem posed by the stable equilibrium of a suspended drop remains nonlinear because of the free boundary where the two surfaces join. A theory based on variational methods is developed on this basis, applying to drops suspended within non-circular frames. The mathematical problem is formulated in §2, and the existence of solutions is proved in §3. Conditions relating to the presence of a free boundary and to the uniqueness of solutions are discussed in §4. To bear out a comment made in part 1 (Benjamin & Cocker, Proc. R. Soc. Lond. . A 394, 19, 1984), the connection between the present topic and a familiar model for confined plasmas is made clear in §5. Finally, in §6, various unresolved aspects of this new topic are reviewed.

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