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

LIU Gong-wei, YANG Kun

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

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

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School of Science, Henan University of Technology, Zhengzhou 450001, China

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.

Received date: 2023-07-22

Online published: 2024-03-30

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).

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

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