Applied Mathematics and Optimization, Vol.50, No.2, 143-159, 2004
Heat conduction with flux condition on a free patch
A new free boundary or free patch problem for the heat equation is presented. In the problem a nonlinear heat flux condition is prescribed on a free portion of the boundary, the patch, the position of which depends on the solution. The existence of a weak solution is established using the theory of set-valued pseudomonotone operators.