边界退化的半线性抛物方程解的渐近行为  

Asymptotic Behavior of Solutions to SemilinearParabolic Equations with Boundary Degeneracy

作　　者：郭微[1] 靳曼莉[1] 井鑫鑫 GUO Wei;JIN Manli;JING Xinxin(School of Mathematics and Statistics,Beihua University,Jilin 132013,Jilin Province,China;College of Mathematics and Systems Science,Shandong University of Science and Technology,Qingdao 266590,Shandong Province,China)

机构地区：[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

出　　处：《吉林大学学报（理学版）》2023年第4期801-807,共7页Journal of Jilin University:Science Edition

基　　金：吉林省教育厅科学技术研究项目(批准号:JJKH20210031KJ,JJKH20210029KJ).

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.We studied the asymptotic behavior of solutions for a class of initial-boundary value problems of a semilinear parabolic equation w ith 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.

关 键 词：边界退化 临界Fujita指标 半线性抛物方程 

分 类 号：O175.23[理学—数学]