Dalibor Pražák, Charles University in Prague, Faculty of Mathematics and Physics, Department of Mathematical Analysis, Prague, Czech Republic
Joint work with T. Bárta and V. Janecek
We consider stationary heat transfer near 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 the means of 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.

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