Dissipation enhancement for a degenerated parabolic equation

This is the authors' abstract. We don't add key points for this paper.

In this paper, we quantitatively consider the enhanced-dissipation effect of the advection term to the parabolic p-Laplacian equations. More precisely, we show the mixing property of flow for the passive scalar enhances the dissipation process of the p-Laplacian in the sense of L² decay, that is, the L² decay can be arbitrarily fast. The main ingredient of our argument is to understand the underlying iteration structure inherited from the parabolic p-Laplacian equations. This extends the dissipation enhancement result of the advection diffusion equation by Yuanyuan Feng and Gautam Iyer into a non-linear setting.