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| Format: | Preprint |
| Published: |
2019
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/1903.05329 |
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| _version_ | 1866914140828729344 |
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| author | Man, Shoudong |
| author_facet | Man, Shoudong |
| contents | In this paper, we study the gradient estimates for the positive solutions of the weighted porous medium equation $$Δu^{m}=δ(x)u_{t}+ψu^{m}$$ on graphs for $m>1$, which is a nonlinear version of the heat equation. Moreover, as applications, we derive a Harnack inequality and the estimates of the porous medium kernel on graphs. The obtained results extend the results of Y. Lin, S. Liu and Y. Yang for the heat equation [8, 9]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1903_05329 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Gradient estimates for the weighted porous medium equation on graphs Man, Shoudong Differential Geometry In this paper, we study the gradient estimates for the positive solutions of the weighted porous medium equation $$Δu^{m}=δ(x)u_{t}+ψu^{m}$$ on graphs for $m>1$, which is a nonlinear version of the heat equation. Moreover, as applications, we derive a Harnack inequality and the estimates of the porous medium kernel on graphs. The obtained results extend the results of Y. Lin, S. Liu and Y. Yang for the heat equation [8, 9]. |
| title | Gradient estimates for the weighted porous medium equation on graphs |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/1903.05329 |