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

doi:10.13371/j.cnki.chin.q.j.m.2024.01.010

Chinese Quarterly Journal of Mathematics ›› 2024, Vol. 39 ›› Issue (1): 97-110.doi: 10.13371/j.cnki.chin.q.j.m.2024.01.010

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).

Abstract

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

CLC Number:

O175.2

LIU Gong-wei, YANG Kun. Finite Time Blow-Up and Global Existence for Degenerate Parabolic Equations at High Initial Energy[J]. Chinese Quarterly Journal of Mathematics, 2024, 39(1): 97-110.

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

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