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

Date

2022-06-28

Authors

Chang, Caihong
Zhang, Zhengce

Journal Title

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Publisher

Texas State University, Department of Mathematics

Abstract

This 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.

Description

Keywords

Matched expansion, Weighted term, Stabilization, Grow up rate, Degeneracy

Citation

Chang, 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.

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Attribution 4.0 International

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