Nonexistence of Type II Blowup for Heat Equation with Exponential Nonlinearity

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.

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Acknowledgement

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

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Correspondence to Shan Li.

Additional information

This work was supported by the National Natural Science Foundation of China (Nos. 41304111, 71372189) and the Department of Science and Technology of Sichuan Province (No. 2017JY0206).

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Ji, R., Li, S. & Chen, H. Nonexistence of Type II Blowup for Heat Equation with Exponential Nonlinearity. Chin. Ann. Math. Ser. B 40, 309–320 (2019). https://doi.org/10.1007/s11401-019-0134-8

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Keywords

  • Nonlinear heat equation
  • Type II blowup
  • Exponential nonlinearity

2000 MR Subject Classification

  • 35K55
  • 35B44
  • 35K05