Ancient caloric functions and parabolic frequency on graphs
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866912162094514176 |
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| author | Lee, Tang-Kai Mohandas, Archana |
| author_facet | Lee, Tang-Kai Mohandas, Archana |
| contents | We study ancient solutions to discrete heat equations on some weighted graphs. On a graph of the form of a product with $\bb Z,$ we show that there are no non-trivial ancient solutions with polynomial growth. This result is parallel to the case of finite graphs, which is also discussed. Along the way, we prove a backward uniqueness result for solutions with appropriate decaying rate based on a monotonicity formula of parabolic frequency. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_15145 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Ancient caloric functions and parabolic frequency on graphs Lee, Tang-Kai Mohandas, Archana Analysis of PDEs Combinatorics We study ancient solutions to discrete heat equations on some weighted graphs. On a graph of the form of a product with $\bb Z,$ we show that there are no non-trivial ancient solutions with polynomial growth. This result is parallel to the case of finite graphs, which is also discussed. Along the way, we prove a backward uniqueness result for solutions with appropriate decaying rate based on a monotonicity formula of parabolic frequency. |
| title | Ancient caloric functions and parabolic frequency on graphs |
| topic | Analysis of PDEs Combinatorics |
| url | https://arxiv.org/abs/2412.15145 |