Discrete Morse Flow for Yamabe Type Heat Flows

Abstract

In this paper, we study the discrete Morse flow for  either Yamabe type heat flow or nonlinear heat flow on a bounded regular domain in the whole space. We show that under suitable assumptions on the initial data $g$ one has a weak approximate discrete Morse flow for the Yamabe type heat flow  on any time interval. This phenomenon is very different from the smooth Yamabe flow, where the finite time blow up may exist.