一类具超临界源的非线性黏弹性双曲方程解的爆破时间下界估计

吉林大学学报(理学版) ›› 2019, Vol. 57 ›› Issue (2): 324-326.

一类具超临界源的非线性黏弹性双曲方程解的爆破时间下界估计

曹春玲^1, 李行^2, 李雨桐^3, 蔡华¹

1. 吉林大学数学学院, 长春 130012; 2. 国网山东省电力公司阳信供电公司, 山东阳信 251800;3. 北京工业大学耿丹学院, 北京 101301

收稿日期:2018-08-22 出版日期:2019-03-26 发布日期:2019-03-26
通讯作者: 曹春玲 E-mail:caocl@jlu.edu.cn

Estimate of a Lower Bound of BlowUp Time for Solutions to a Class ofNonlinear Viscoelastic Hyperbolic Equations with Supercritical Sources#br#

CAO Chunling¹, LI Hang², LI Yutong³, CAI Hua¹

1. College of Mathematics, Jilin University, Changchun 130012, China; 2. Yangxin Power Supply Company,State Grid Shandong Electric Power Company, Yangxin 251800, Shandong Province, China;3. Gengdan Institute of Beijing University of Technology, Beijing 101301, China

Received:2018-08-22 Online:2019-03-26 Published:2019-03-26
Contact: CAO Chunling E-mail:caocl@jlu.edu.cn

摘要/Abstract

摘要： 考虑一类涉及超临界源项的非线性黏弹性双曲方程解的爆破时间下界估计，通过构造带阻尼项的控制函数, 利用能量估计方法和Sobolev嵌入定理, 得到了该问题解爆破时间的显式下界估计.

关键词: 黏弹性双曲方程, 能量估计法, 下界估计；爆破时间

Abstract: We considered estimate of a lower bound of blow-up time for solutions to a class of nonlinear viscoelastic hyperbolic equations involving supercritical source terms. By constructing the control function with damping term, using the mehtod of energy estimate and Sobolev embedding theorem, we obtained an explicit estimate of lower bound of the blow-up time for the solutions to the problem.

Key words: viscoelastic hyperbolic equation, method of energy estimate, estimate of lower bound, blow-up time

中图分类号:

O175.27

曹春玲, 李行, 李雨桐, 蔡华. 一类具超临界源的非线性黏弹性双曲方程解的爆破时间下界估计[J]. 吉林大学学报(理学版), 2019, 57(2): 324-326.

CAO Chunling, LI Hang, LI Yutong, CAI Hua. Estimate of a Lower Bound of BlowUp Time for Solutions to a Class ofNonlinear Viscoelastic Hyperbolic Equations with Supercritical Sources#br#[J]. Journal of Jilin University Science Edition, 2019, 57(2): 324-326.

[1]	陈洁姝, 金鑫. 具强阻尼项的四阶弱耦合双曲方程组解爆破时间的下界估计[J]. 吉林大学学报(理学版), 2020, 58(4): 864-867.
[2]	王雪, 郭悦, 祖阁. 一类具超临界源非线性双曲方程解的爆破时间下界估计[J]. 吉林大学学报(理学版), 2019, 57(3): 567-570.