arXiv
Open Access
2024
Ancient caloric functions and parabolic frequency on graphs
Tang-Kai Lee
Archana Mohandas
Abstrak
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.
Penulis (2)
T
Tang-Kai Lee
A
Archana Mohandas
Akses Cepat
Informasi Jurnal
- Tahun Terbit
- 2024
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- en
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- arXiv
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- Open Access ✓