2024/12/19 by Tang-Kai Lee, Lee, Tang-Kai, Archana Mohandas +1
Physics and Astronomy · #Advanced Mathematical Theories and Applications
paper · pdf · doi:10.48550/arxiv.2412.15145
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.