一类退化抛物方程高初始能量下解的有限时刻爆破及整体存在性  

Finite Time Blow-Up and Global Existence for Degenerate Parabolic Equations at High Initial Energy

作　　者：刘功伟 杨坤 LIU Gong-wei;YANG Kun(School of Science,Henan University of Technology,Zhengzhou 450001,China)

机构地区：[1]School of Science,Henan University of Technology,Zhengzhou 450001,China

出　　处：《Chinese Quarterly Journal of Mathematics》2024年第1期97-110,共14页数学季刊（英文版）

基　　金：Supported by National Natural Science Foundation of China(Grant No.11801145);the Innovative Funds Plan of Henan University of Technology(Grant No.2020ZKCJ09)。

摘　　要：We consider the initial-boundary value problem for finitely degenerate parabolic equation. We first give sufficient conditions for the blow-up and global existence of the parabolic equation at high initial energy level. Then, we establish the existence of solutions blowing up in finite time with initial data at arbitrary energy level. Finally, we estimate the upper bound of the blow-up time under certain conditions.

关 键 词：High energy Degenerate parabolic equations Blow up Global existence 

分 类 号：O175.2[理学—数学]