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

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

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

刘功伟, 杨坤

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

LIU Gong-wei, YANG Kun

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).

摘要/Abstract

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

中图分类号:

O175.2

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.

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.

[1]	秦玉明, 刘子丽. 第三型热弹Timoshenko型方程组指数衰减 [J]. 数学季刊, 2019, 34(2): 111-125.
[2]	李姣龙, 秦玉明. 热弹系统解的整体存在性、渐近性和一致吸引子[J]. 数学季刊, 2017, 32(3): 221-237.
[3]	郑秀珍, 秦玉明. 非自治Timoshenko系统解的整体存在性和渐进性[J]. 数学季刊, 2017, 32(3): 246-254.
[4]	胡文松, 秦玉明. 关于衰减Timoshenko系统的解的整体存在性、渐近性及一致吸引子[J]. 数学季刊, 2017, 32(3): 305-321.
[5]	郑秀珍. Timoshenko系统在Gurtin-Pipkin热能定律下解的整体存在性、渐进性及一致吸引子[J]. 数学季刊, 2016, 31(3): 307-330.
[6]	冯保伟, 张明, 梁铁旺, 李海燕. 强耗散可拉伸梁方程解的一致衰减性[J]. 数学季刊, 2014, 29(1): 151-158.
[7]	马志勇, 张凌瑞. 带有记忆的热弹盘问题解的整体存在性[J]. 数学季刊, 2012, 27(3): 382-388.
[8]	郭红霞, 韩献军. 一类非线性拟抛物方程的初边值问题 [J]. 数学季刊, 2010, 25(3): 335-343.
[9]	崔国忠, 高艳玲, 郭从洲. 一类具非局部源的退化反应扩散方程的爆破性质[J]. 数学季刊, 2010, 25(3): 352-359.
[10]	秦玉明, 黄兰, 马志勇等. 对高维热粘弹方程组解的整体存在性的注记[J]. 数学季刊, 2009, 24(2): 159-167.
[11]	秦玉明, 马志勇, 黄兰. 对具有非单调压力的非线性热粘弹方程在H⁴中解的整体存在性的注记[J]. 数学季刊, 2007, 22(4): 607-611.
[12]	庞进生, 张宏伟. 拟线性抛物方程整体解的存在性和不存在性[J]. 数学季刊, 2007, 22(3): 444-450.
[13]	吴中林, 徐娟娟. 一维非单调流体模型在H²中解的整体存在性[J]. 数学季刊, 2007, 22(2): 296-304.
[14]	陈守信, 韩小森. 半导体中一维拟中性漂流扩散模型整体光滑解的渐进性[J]. 数学季刊, 2006, 21(3): 385-396.
[15]	叶耀军, 刘秋香. 一类双退化非线性抛物型方程[J]. 数学季刊, 2005, 20(4): 390-394.

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

PDF (PC)

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

第三型热弹Timoshenko型方程组指数衰减

一类非线性拟抛物方程的初边值问题

编辑推荐

Metrics

本文评价