数学季刊 ›› 2024, Vol. 39 ›› Issue (1): 97-110.doi: 10.13371/j.cnki.chin.q.j.m.2024.01.010

• • 上一篇    

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

  

  1. School of Science, Henan University of Technology, Zhengzhou 450001, China
  • 收稿日期:2023-07-22 出版日期:2024-03-30 发布日期:2024-03-30
  • 通讯作者: LIU Gong-wei (1983-), male, native of Xinyang, Henan, associate professor of Henan University of Technology, engages in PDE; E-mail:gongweiliu@126.com
  • 作者简介:LIU Gong-wei (1983-), male, native of Xinyang, Henan, associate professor of Henan University of Technology, engages in PDE; YANG Kun (1998-), female, native of Jiaozuo, Henan, graduate student of Henan University of Technology, engages in PDE.
  • 基金资助:
    Supported by National Natural Science Foundation of China (Grant No. 11801145) and the
    Innovative Funds Plan of Henan University of Technology (Grant No. 2020ZKCJ09).

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

  1. School of Science, Henan University of Technology, Zhengzhou 450001, China
  • Received:2023-07-22 Online:2024-03-30 Published:2024-03-30
  • Contact: LIU Gong-wei (1983-), male, native of Xinyang, Henan, associate professor of Henan University of Technology, engages in PDE; E-mail:gongweiliu@126.com
  • About author:LIU Gong-wei (1983-), male, native of Xinyang, Henan, associate professor of Henan University of Technology, engages in PDE; YANG Kun (1998-), female, native of Jiaozuo, Henan, graduate student of Henan University of Technology, engages in PDE.
  • Supported by:
    Supported by National Natural Science Foundation of China (Grant No. 11801145) and the
    Innovative Funds Plan of Henan University of Technology (Grant No. 2020ZKCJ09).

PDF (PC)

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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

Abstract: 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.

Key words:  High energy, Degenerate parabolic equations, Blow up, Global existence

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