一类时空分数阶伪抛物方程解的存在与爆破

陈业明; 李亚宁

doi:10.21656/1000-0887.450217

一类时空分数阶伪抛物方程解的存在与爆破

doi: 10.21656/1000-0887.450217

陈业明,
李亚宁^,

南京信息工程大学数学与统计学院，南京 210044

基金项目:

国家自然科学基金 11801276

详细信息

作者简介:
陈业明(2000—)，男，硕士(E-mail: 2082725007@qq.com)

通讯作者:
李亚宁(1985—)，女，副教授(通讯作者. E-mail: liyaning@nuist.edu.cn)

中图分类号: O357.41
计量
- 文章访问数: 67
- HTML全文浏览量: 21
- PDF下载量: 11
- 被引次数: 0
出版历程
- 收稿日期: 2024-07-17
- 修回日期: 2024-10-10
- 刊出日期: 2025-11-01

Existence and Blow-Up of Solutions to a Class of Time-Space Fractional Pseudo-Parabolic Equations

CHEN Yeming,
LI Yaning^,

School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, P.R.China

摘要

摘要: 研究了非齐次项对一类时空分数阶伪抛物方程解的存在与爆破的影响. 首先，用不动点定理得到适度解的局部存在性，再运用检验函数法得到，在一定条件下方程的解有限时间爆破；最后，证明存在合适的初值和非齐次项使得方程的解全局存在. 该结论拓展了整数阶伪抛物方程对应的结果，同时，与非齐次项为0时的时空分数阶伪抛物方程对应的结论不同，说明了非齐次项对解的爆破和全局存在有一定的影响.
- 时空分数阶伪抛物方程 /
- 适度解 /
- 局部存在性 /
- 爆破 /
- 全局存在性
Abstract: The effects of the inhomogeneity on the existence and finite time blow-up of solutions to a class of time-space fractional pseudo-parabolic equations were analyzed. Firstly, the local existence of the mild solution was obtained with the fixed-point theorem. By means of the test function method, the solutions' finite-time blow-up was educed under certain conditions. The global existence of the solution to the equation was proved under suitable initial data and inhomogeneous terms. The findings extend the corresponding solution results of integral-order pseudo-parabolic equations, but differ from those of the time-space fractional pseudo-parabolic equations with zero inhomogeneous terms, and show the effects of inhomogeneous terms on the existence and blow-up of the solutions.
- time-space fractional pseudo-parabolic equation /
- mild solution /
- local existence /
- blow-up /
- global existence

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参考文献(17)

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