TY  - JOUR
T1  - Heat conduction problem of an evaporating liquid wedge
A1  - Bárta, Tomáš
A1  - Janeček, V.
A1  - Pražák, Dalibor
JA  - Electron. J. Diff. Equ.
Y1  - 2015
VL  - 2015
IS  - 53
U2  - Chapter: 1 - 18
N2  - 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 re- formulate 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.
M1  - Preprint project = NCMM
M1  - Preprint year = 2014
M1  - Preprint number = 24
M1  - Preprint ID = NCMM/2014/24
ER  -