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

刘功伟, 杨坤

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

数学季刊 >

2024 , Vol. 39 >Issue 1: 97 - 110

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

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

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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.

收稿日期: 2023-07-22

网络出版日期: 2024-03-30

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).

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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

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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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

本文引用格式

刘功伟, 杨坤 . 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[J]. 数学季刊, 2024 , 39(1) : 97 -110 . DOI: 10.13371/j.cnki.chin.q.j.m.2024.01.010

Abstract

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

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