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 u _t = Δu + e ^u in ℝ ^N. 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

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