边界退化的半线性抛物方程解的渐近行为

吉林大学学报(理学版) ›› 2023, Vol. 61 ›› Issue (4): 801-807.

边界退化的半线性抛物方程解的渐近行为

郭微¹, 靳曼莉¹, 井鑫鑫²

1. 北华大学数学与统计学院, 吉林吉林 132013; 2. 山东科技大学数学与系统科学学院, 山东青岛 266590

收稿日期:2022-10-24 出版日期:2023-07-26 发布日期:2023-07-26
通讯作者: 靳曼莉 E-mail:64278144@qq.com

Asymptotic Behavior of Solutions to Semilinear Parabolic Equations with Boundary Degeneracy

GUO Wei¹, JIN Manli¹, JING Xinxin²

1. School of Mathematics and Statistics, Beihua University, Jilin 132013, Jilin Province, China;
2. College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, Shandong Province, China

Received:2022-10-24 Online:2023-07-26 Published:2023-07-26

摘要/Abstract

摘要： 用加权能量估计和构造自相似上解的方法, 研究一类在边界退化的半线性抛物方程初边值问题解的渐近行为, 得到了问题解的整体存在性和爆破性, 建立了Fujita型定理, 并刻画了临界Fujita指标与退化扩散项和非线性源项之间的定量关系.

关键词: 边界退化, 临界Fujita指标, 半线性抛物方程

Abstract: We studied the asymptotic behavior of solutions for a class of initial-boundary value problems of a semilinear parabolic equation with boundary degeneracy by using the methods of weighted energy estimates and constructing self-similar upper solutions. We obtained the global existence and blowing-up properties of solutions to the problem, established Fujita type theorem, and characterized the quantitative relationship between the critical Fujita exponent and the degenerate diffusion term and the nonlinear source term.

Key words: , boundary degeneracy, critical Fujita exponent, semilinear parabolic equation

中图分类号:

郭微, 靳曼莉, 井鑫鑫. 边界退化的半线性抛物方程解的渐近行为[J]. 吉林大学学报(理学版), 2023, 61(4): 801-807.

GUO Wei, JIN Manli, JING Xinxin. Asymptotic Behavior of Solutions to Semilinear Parabolic Equations with Boundary Degeneracy[J]. Journal of Jilin University Science Edition, 2023, 61(4): 801-807.

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