On a boundary value problem in a degenerate region with a boundary moving in a self-similar laws

Abstract

In work the regional task for the heat conductivity equation in area with mobile borders is considered. Thus the area degenerates in a point in an initial timepoint. The task is reduced by method of thermal potentials to the special integrated equation like Voltaire. It is shown that the uniform integrated equation has one nonzero decision, but thus the corresponding uniform task has only the trivial decision.