Chang, CaihongZhang, Zhengce2023-04-182023-04-182022-06-28Chang, C., & Zhang, Z. (2022). Asymptotic behavior of blowup solutions for Henon type parabolic equations with exponential nonlinearity. <i>Electronic Journal of Differential Equations, 2022</i>(42), pp. 1-19.1072-6691https://hdl.handle.net/10877/16601This article concerns the blow up behavior for the Henon type parabolic equation with exponential nonlinearity, ut = Δu + |x|σ eu in BR x ℝ+, where σ ≥ 0 and BR = {x ∈ ℝN : |x| < R}. We consider all cases in which blowup of solutions occurs, i.e. N ≥ 10 + 4σ. Grow up rates are established by a certain matching of different asymptotic behaviors in the inner region (near the singularity) and the outer region (close to the boundary). For the cases N > 10 + 4σ and N = 10 + 4σ, 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.Text19 pages1 file (.pdf)enAttribution 4.0 InternationalMatched expansionWeighted termStabilizationGrow up rateDegeneracyArticle