Approaching a vertex in a shrinking domain under a nonlinear flow

We consider the asymptotic behaviour of the solutions of the homogeneous Dirichlet problem for a nonlinear degenerate parabolic equation related to the porous medium equation in a noncylindrical domain in space-time shrinking to a point. The study is motivated by the classical analysis of regular and irregular points for the heat equation. We describe the asymptotics of the maximal solution approaching the vertex by means of matched asymptotic expansion techniques.