Semilinear Li & Yau inequalities
Analysis of PDEs
2022-01-10 v1 Differential Geometry
Abstract
We derive an adaptation of Li & Yau estimates for positive solutions of semilinear heat equations on Riemannian manifolds with nonnegative Ricci tensor. We then apply these estimates to obtain a Harnack inequality and to discuss monotonicity, convexity, decay estimates and triviality of ancient and eternal solutions.
Cite
@article{arxiv.2201.02530,
title = {Semilinear Li & Yau inequalities},
author = {Daniele Castorina and Giovanni Catino and Carlo Mantegazza},
journal= {arXiv preprint arXiv:2201.02530},
year = {2022}
}