A class of semilinear heat flows with general nonlinear reaction terms is considered on complete Riemannian manifolds with Ricci curvature bounded from below. Two types of (space-time and space only) gradient estimates are established for positive solutions to the flow, and the corresponding Harnack inequalities are obtained to allow for comparison of solutions. Some specific examples of the reaction term such as logarithmic reaction, Fisher-KPP and Allen-Cahn equations are discussed as applications of the estimates so derived. Referring to logarithmic nonlinearities, some discussions are made on Liouville type properties of bounded solutions.

一类具有一般非线性反应项的半线性热流被考虑在完全黎曼流形上，其中 Ricci 曲率从下方有界。为流的正解建立了两种类型的（仅时空和空间）梯度估计，并获得了相应的 Harnack 不等式以允许对解进行比较。反应项的一些具体例子，如对数反应、Fisher-KPP 和 Allen-Cahn 方程，作为如此导出的估计的应用进行了讨论。参考对数非线性，对有界解的Liouville型性质进行了一些讨论。