Discrete Morse Flow for Yamabe Type Heat Flows

descriptionPublicationkeyboard_double_arrow_right Article 01 Jun 2023Publisher:Global Science PressJournal:Journal of Partial Differential Equations, volume 36, pages 48-57 (issn: 1000-940X, eissn: 2079-732X,

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Authors: Li, Ma; Zheng, Wei;

doi: 10.4208/jpde.v36.n1.3

Discrete Morse Flow for Yamabe Type Heat Flows

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Abstract

Summary: 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.

Keywords

critical exponent, nonlinear heat flow, discrete Morse flow, Heat equation, Yamabe type flow, Geometric evolution equations

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