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Chinese Annals of Mathematics, Series B

, Volume 40, Issue 2, pp 309–320 | Cite as

Nonexistence of Type II Blowup for Heat Equation with Exponential Nonlinearity

  • Ruihong Ji
  • Shan LiEmail author
  • Hui Chen
Article
  • 12 Downloads

Abstract

This paper deals with the blowup behavior of the radially symmetric solution of the nonlinear heat equation ut = Δu + eu in ℝN. The authors show the nonexistence of type II blowup under radial symmetric case in the lower supercritical range 3 ≤ N ≤ 9, and give a sufficient condition for the occurrence of type I blowup. The result extends that of Fila and Pulkkinen (2008) in a finite ball to the whole space.

Keywords

Nonlinear heat equation Type II blowup Exponential nonlinearity 

2000 MR Subject Classification

35K55 35B44 35K05 

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Notes

Acknowledgement

The authors would like to thank the referees for their helpful comments on the manuscript.

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Copyright information

© Fudan University and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Geomathematics Key Laboratory of Sichuan ProvinceChengdu University of TechnologyChengduChina
  2. 2.Business SchoolSichuan UniversityChengduChina

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