@article{Ascione2023, 
author = {Giacomo Ascione and Daniele Castorina and Giovanni Catino and Carlo Mantegazza},
title = {A matrix Harnack inequality for semilinear heat equations},
year = {2023},
journal = {Mathematics in Engineering},
volume = {5},
number = {1},
pages = {1-15},
keywords = {ancient solution, eternal solution, semilinear heat equation, matrix Harnack inequality},
url = {https://www.sciopen.com/article/10.3934/mine.2023003},
doi = {10.3934/mine.2023003},
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 [5] 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.}
}