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arXiv · 2104.12578

Dissipation enhancement for a degenerated parabolic equation

Yu Feng·Bingyang Hu·Xiaoqian Xu
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Abstract

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 $L^2$ decay, that is, the $L^2$ 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.

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Yu Feng, Bingyang Hu, Xiaoqian Xu. 2021-04-26. Dissipation enhancement for a degenerated parabolic equation. https://doi.org/10.4310/cms.2023.v21.n1.a8

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