Conditions for instantaneous support shrinking and sharp estimates for the support of the solution of the Cauchy problem for a doubly non-linear parabolic equation with absorption

Instantaneous support shrinking is studied for a doubly nonlinear degenerate parabolic equation in the case of slow diffusion when, in general, the Cauchy initial data are Radon measures. For a non-negative solution, a necessary and sufficient condition for instantaneous support shrinking is obtained in terms of the local behaviour of the mass of the initial data. In the same terms, estimates are obtained for the size of the support, that are sharp with respect to order.