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

This article concerns the blow up behavior for 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 \(B_R=\{x\in\mathbb{R}^N: |x|<R\}\).We consider all cases in which blowup of solutions occurs, i.e. \(N\geq 10+4\sigma\).Grow rates are established by a certain matching different asymptotic behaviorsin inner region (near singularity) outer (close to boundary).For \(N>10+4\sigma\) \(N=10+4\sigma\), expansions stationary have forms, so two discussed separately. Moreover, widths also obtained.