(1) Department of Mathematics, Brigham Young University, Provo, UT 84602, USA;(2) Department of Mathematics and Statistics, Oakland University, Rochester, MI 48309, USA
Abstract:
A new free boundary or free patch problem for the heat equation ispresented. In the problem a nonlinear heat flux condition is prescribed on afree portion of the boundary, the patch, the position of which depends onthe solution. The existence of a weak solution is established using thetheory of set-valued pseudomonotone operators.
