Instantaneous support shrinking phenomenon in the case of fast diffusion for a doubly nonlinear parabolic equation with absorption

Abstract

We study the instantaneous support shrinking phenomenon for a doubly nonlinear parabolic equation in the fast diffusion case. The initial data of the Cauchy problem are locally finite Radon measures. We obtain for nonnegative solutions necessary and sufficient condition for instantaneous support shrinking phenomenon in terms of local behavior of the initial data. In the same terms we express sharp with respect to rate bilateral estimates for the size of the support.