DISSIPATION ENHANCEMENT FOR A DEGENERATED PARABOLIC EQUATION

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 to a non-linear setting.

Duke Scholars

Author Xiaoqian Xu DKU Faculty