Nonexistence of Type II Blowup for Heat Equation with Exponential Nonlinearity


Ruihong JI,Shan LI,Hui CHEN.Nonexistence of Type II Blowup for Heat Equation with Exponential Nonlinearity[J].Chinese Annals of Mathematics B,2019,40(2):309~320
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Ruihong JI; Shan LI;Hui CHEN


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).
Abstract: This paper deals with the blowup behavior of the radially symmetric solution of the nonlinear heat equation $u_t=\Delta u+\rme^u$ in $\mathbb{R}^N$. The authors show the nonexistence of type II blowup under radial symmetric case in the lower supercritical range $3\leq N\leq9$, 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.


Nonlinear heat equation, Type II blowup, Exponentialnonlinearity


35K55, 35B44, 35K05
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