Gradient Estimates for Nonlinear Reaction–Diffusion Equations on Riemannian Manifolds

In this paper, we obtain the global Li–Yau type gradient estimate and Hamilton type estimate for positive solutions to the nonlinear reaction diffusion equation ut=Δpuγ+cuq\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} u_t=\Delta _pu^{\gamma }+cu^{q} \end{aligned}$$\end{document}on compact Riemannian manifolds with nonnegative Ricci curvature. As applications, the corresponding Harnack inequalities are derived.