Discrete Morse Flow for Yamabe Type Heat Flows

. 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 approxi-mate 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.