Electron. J. Diff. Equ.,
Vol. 2015 (2015), No. 53, pp. 1-18.
Heat conduction problem of an evaporating liquid wedge
Tomas Barta, Vladislav Janecek, Dalibor Prazak
Abstract:
We consider the stationary heat transfer near the contact line of an
evaporating liquid wedge surrounded by the atmosphere of its
pure vapor. In a simplified setting, the problem reduces to the
Laplace equation in a half circle, subject to a non-homogeneous
and singular boundary condition.
By classical tools (conformal mapping, Green's function), we reformulate
the problem as an integral equation for the unknown Neumann boundary
condition in the setting of appropriate fractional Sobolev and weighted space.
The unique solvability is then obtained by means of the Fredholm theorem.
Submitted December 17, 2014. Published February 26, 2015.
Math Subject Classifications: 80A20, 45B05, 45E05.
Key Words: Liquid wedge evaporation; heat transfer; laplace equation;
singular boundary conditions.
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Tomas Barta
Charles University in Prague,
Faculty of Mathematics and Physics
Department of Mathematical Analysis,
Sokolovska 83
186 75 Prague 8, Czech Republic
email: barta@karlin.mff.cuni.cz
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Vladislav Janecek
University Paris-Sud, CNRS, Lab FAST, Bat 502
Campus Universitaire, Orsay F-91405, France.
Arcelor Mittal, Voie Romaine, BP 30320
Maizieres-les-Metz, F-57283, France
email: vladislav.janecek@arcelormittal.com
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Dalibor Prazak
Charles University in Prague,
Faculty of Mathematics and Physics
Department of Mathematical Analysis,
Sokolovska 83
186 75 Prague 8, Czech Republic
email: prazak@karlin.mff.cuni.cz
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