arXiv Open Access 2024

Ancient caloric functions and parabolic frequency on graphs

Tang-Kai Lee Archana Mohandas
Lihat Sumber

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.

Topik & Kata Kunci

Penulis (2)

T

Tang-Kai Lee

A

Archana Mohandas

Format Sitasi

Lee, T., Mohandas, A. (2024). Ancient caloric functions and parabolic frequency on graphs. https://arxiv.org/abs/2412.15145

Akses Cepat

Lihat di Sumber
Informasi Jurnal
Tahun Terbit
2024
Bahasa
en
Sumber Database
arXiv
Akses
Open Access ✓