Hamilton and Souplet-Zhang type estimations on semilinear parabolic system along geometric flow

TL;DR

This paper develops Hamilton and Souplet-Zhang type gradient estimates for semilinear parabolic systems evolving along geometric flows on weighted Riemannian manifolds, advancing the understanding of such systems' behavior.

Contribution

It introduces new gradient estimation techniques for semilinear parabolic systems along geometric flows, extending existing methods to weighted Riemannian manifolds.

Findings

Derived Hamilton type gradient estimates

Established Souplet-Zhang type gradient bounds

Applied estimates to analyze solution behavior

Abstract

In this article we derive both Hamilton type and Souplet-Zhang type gradient estimations for a system of semilinear equations along a geometric flow on a weighted Riemannian manifold.