Dissipation enhancement for a degenerated parabolic equation
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arXiv
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| Format: | Preprint |
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2021
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| _version_ | 1866910327293083648 |
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| author | Feng, Yu Hu, Bingyang Xu, Xiaoqian |
| author_facet | Feng, Yu Hu, Bingyang Xu, Xiaoqian |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2104_12578 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Dissipation enhancement for a degenerated parabolic equation Feng, Yu Hu, Bingyang Xu, Xiaoqian Analysis of PDEs Primary 76R05, Secondary 35B27, 35B44, 35Q35 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. |
| title | Dissipation enhancement for a degenerated parabolic equation |
| topic | Analysis of PDEs Primary 76R05, Secondary 35B27, 35B44, 35Q35 |
| url | https://arxiv.org/abs/2104.12578 |