一类具有正初始能量的双重退化方程解的爆破和爆破时间上界估计  

Blow-up and upper bounds of blow-up time fora doubly degenerate equation with positive initial energy

作　　者：吴秀兰 赵雅鑫 杨晓新 成立波 WU Xiu-lan;ZHAO Ya-xin;YANG Xiao-xin;CHENG Li-bo(School of Mathematics and Statistics,Changchun University of Science and Technology,Changchun 130022,China)

机构地区：[1]长春理工大学数学与统计学院,吉林长春130022

出　　处：《东北师大学报（自然科学版）》2024年第3期22-26,共5页Journal of Northeast Normal University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(12171054).

摘　　要：研究了具有齐次Dirichlet边界条件的双重退化抛物方程u t=div(|Δu^(m)|^(p-2)Δu^(m))+f(u),x∈Ω,t≥0解的爆破问题.利用构造凸函数的方法,证明了f在适当的条件下,r>p>2,m≥1,初始能量为正时,解在有限时刻爆破,并给出了爆破时间的上界估计.该结论推广了已有结果.This paper deals with the blow-up of solutions to the following doubly degenerate parabolic equation u t=div(|Δu^(m)|^(p-2)Δu^(m))+f(u),x∈Ω,t≥0,with homogeneous Dirichlet boundary condition.A blow-up result is established when the initial energy is positive,r>p>2,m≥1,and under suitable conditions on f.Furthermore,a upper bound for blow-up time is also given.This result extends existing results.

关 键 词：爆破 双重退化 正初始能量 爆破上界 

分 类 号：O175.2[理学—数学]