数学物理学报 ›› 2025, Vol. 45 ›› Issue (3): 748-755.

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具有阻尼项的粘弹性波动方程解的高能爆破

李倩*(),邢艳元()   

  1. 长治学院数学系 山西长治 046011
  • 收稿日期:2024-08-19 修回日期:2024-10-28 出版日期:2025-06-26 发布日期:2025-06-20
  • 通讯作者: *李倩, E-mail:liqian206@outlook.com
  • 作者简介:邢艳元, E-mail: czxyxyy@czc.edu.cn
  • 基金资助:
    山西省应用基础研究计划项目(202203021222332);山西省应用基础研究计划项目(202103021223379)

Finite Time Blow up of Solutions for Nonlinear Wave Equation with the Damping Term at Arbitrarily Positive Initial Energy

Li Qian*(),Xing Yanyuan()   

  1. Department of Mathematics, Changzhi University, Shanxi Changzhi 046011
  • Received:2024-08-19 Revised:2024-10-28 Online:2025-06-26 Published:2025-06-20
  • Supported by:
    Fundamental Science Research Projects of Shanxi Province(202203021222332);Fundamental Science Research Projects of Shanxi Province(202103021223379)

摘要:

研究了带有强阻尼项和线性弱阻尼项的粘弹性波动方程的初边值问题在高的初始能级状态下解的有限时间爆破. 利用了凹函数方法找到问题的解在任意正初始能级状态下爆破的充分条件.

关键词: 波动方程, 高初始能级, 爆破, 粘弹性项

Abstract:

This paper studies the finite time blow up of solutions for a initial boundary value problem of a viscoelastic wave equation with the strong damping term and linear weak damping term at high initial energy level. By using the concavity method, we obtain some new sufficient conditions on initial data such that the solution with arbitrarily positive initial energy blows up in finite time.

Key words: wave equation, high initial energy, finite time blow up, viscoelastic term

中图分类号: 

  • O175