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Volume 36, Issue 1
Discrete Morse Flow for Yamabe Type Heat Flows

Li Ma & Wei Zheng

DOI: 10.4208/jpde.v36.n1.3

J. Part. Diff. Eq., 36 (2023), pp. 48-57.

Published online: 2022-12

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  • 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.

  • Keywords

Discrete Morse flow, Yamabe type flow, critical exponent, nonlinear heat flow.

  • AMS Subject Headings

53C44, 35K50, 93C55

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

lma17@ustb.edu.cn (Li Ma)

  • BibTex
  • RIS
  • TXT
@Article{JPDE-36-48, author = {Ma , Li and Zheng , Wei}, title = {Discrete Morse Flow for Yamabe Type Heat Flows}, journal = {Journal of Partial Differential Equations}, year = {2022}, volume = {36}, number = {1}, pages = {48--57}, 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.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v36.n1.3}, url = {http://global-sci.org/intro/article_detail/jpde/21292.html} }
TY - JOUR T1 - Discrete Morse Flow for Yamabe Type Heat Flows AU - Ma , Li AU - Zheng , Wei JO - Journal of Partial Differential Equations VL - 1 SP - 48 EP - 57 PY - 2022 DA - 2022/12 SN - 36 DO - http://doi.org/10.4208/jpde.v36.n1.3 UR - https://global-sci.org/intro/article_detail/jpde/21292.html KW - Discrete Morse flow, Yamabe type flow, critical exponent, nonlinear heat flow. AB -

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.

Li Ma & Wei Zheng. (2022). Discrete Morse Flow for Yamabe Type Heat Flows. Journal of Partial Differential Equations. 36 (1). 48-57. doi:10.4208/jpde.v36.n1.3
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