Asymptotic behavior of blowup solutions for Henon type parabolic equations with exponential nonlinearity

Abstract

This article concerns the blow up behavior for the Henon type parabolic equation withexponential nonlinearity, $$ u_t=\Delta u+|x|^{\sigma}e^u\quad \text{in } B_R\times \mathbb{R}_+, $$ where \(\sigma\geq 0\) and \(B_R=\{x\in\mathbb{R}^N: |x|10+4\sigma\) and \(N=10+4\sigma\), the asymptotic expansions of stationary solutions have different forms, so two cases are discussed separately. Moreover, different inner region widths in two cases are also obtained.