A matrix Harnack inequality for semilinear heat equations
Analysis of PDEs
2021-07-30 v1 Differential Geometry
Abstract
We derive a matrix version of Li \& Yau--type estimates for positive solutions of semilinear heat equations on Riemannian manifolds with nonnegative sectional curvatures and parallel Ricci tensor, similarly to what R.~Hamilton did in~\cite{hamilton7} for the standard heat equation. We then apply these estimates to obtain some Harnack--type inequalities, which give local bounds on the solutions in terms of the geometric quantities involved.
Keywords
Cite
@article{arxiv.2107.13846,
title = {A matrix Harnack inequality for semilinear heat equations},
author = {Giacomo Ascione and Daniele Castorina and Giovanni Catino and Carlo Mantegazza},
journal= {arXiv preprint arXiv:2107.13846},
year = {2021}
}