Large time behavior of the solution to the Cauchy problem for the discrete p-Laplacian with density on infinite graphs
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909975517855744 |
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| author | Tedeev, Alan A. |
| author_facet | Tedeev, Alan A. |
| contents | We consider the Cauchy problem for the nonstationary discrete p-Laplacian with inhomogeneous density \r{ho}(x) on an infinite graph which supports the Sobolev inequality. For nonnegative solutions when p > 2, we prove the precise rate of stabilization in time, provided \r{ho}(x) is a non-power function. When p > 2 and \r{ho}(x) goes to zero fast enough, we prove the universal bound. Our technique relies on suitable energy inequalities and a new embedding result. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_21321 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Large time behavior of the solution to the Cauchy problem for the discrete p-Laplacian with density on infinite graphs Tedeev, Alan A. Analysis of PDEs 2020: Primary 35R02, Secondary 39A12, 58J35 We consider the Cauchy problem for the nonstationary discrete p-Laplacian with inhomogeneous density \r{ho}(x) on an infinite graph which supports the Sobolev inequality. For nonnegative solutions when p > 2, we prove the precise rate of stabilization in time, provided \r{ho}(x) is a non-power function. When p > 2 and \r{ho}(x) goes to zero fast enough, we prove the universal bound. Our technique relies on suitable energy inequalities and a new embedding result. |
| title | Large time behavior of the solution to the Cauchy problem for the discrete p-Laplacian with density on infinite graphs |
| topic | Analysis of PDEs 2020: Primary 35R02, Secondary 39A12, 58J35 |
| url | https://arxiv.org/abs/2512.21321 |