Li-Yau type estimation of a semilinear parabolic system along geometric flow

Abstract

Abstract This article provides a Li–Yau-type gradient estimate for a semilinear weighted parabolic system of semilinear equations along an abstract geometric flow on a smooth measure space. A Harnack-type inequality on the system is also derived at the end.

Keywords

• Gradient estimate
• Weighted Laplacian
• Parabolic system
• Geometric flow
• Li-Yau type estimation