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带有强阻尼时滞项的m-Laplacian型波方程解的爆破

高云龙 林荣瑞 佘连兵 李爱静

高云龙, 林荣瑞, 佘连兵, 李爱静. 带有强阻尼时滞项的m-Laplacian型波方程解的爆破[J]. 华南师范大学学报(自然科学版), 2021, 53(1): 94-99. doi: 10.6054/j.jscnun.2021015
引用本文: 高云龙, 林荣瑞, 佘连兵, 李爱静. 带有强阻尼时滞项的m-Laplacian型波方程解的爆破[J]. 华南师范大学学报(自然科学版), 2021, 53(1): 94-99. doi: 10.6054/j.jscnun.2021015
GAO Yunlong, LIN Rongrui, SHE Lianbing, LI Aijing. Blow-up of Solutions to the m-Laplacian Type Wave Equation with Strong Delay Terms[J]. Journal of South China normal University (Natural Science Edition), 2021, 53(1): 94-99. doi: 10.6054/j.jscnun.2021015
Citation: GAO Yunlong, LIN Rongrui, SHE Lianbing, LI Aijing. Blow-up of Solutions to the m-Laplacian Type Wave Equation with Strong Delay Terms[J]. Journal of South China normal University (Natural Science Edition), 2021, 53(1): 94-99. doi: 10.6054/j.jscnun.2021015

带有强阻尼时滞项的m-Laplacian型波方程解的爆破

doi: 10.6054/j.jscnun.2021015
基金项目: 

国家自然科学基金项目 11571283

贵州省教育厅自然基金项目 黔教合KY字[2019]139

贵州省教育厅自然基金项目 黔教合KY字[2019]143)

六盘水师范学院校级项目 LPSSYKYJJ201801

六盘水师范学院校级项目 LPSSKJTD201907

详细信息
    通讯作者:

    高云龙, Email: gyl0813101x@163.com

  • 中图分类号: O175.2

Blow-up of Solutions to the m-Laplacian Type Wave Equation with Strong Delay Terms

  • 摘要: 研究带有强阻尼时滞项的m-Laplacian型波方程: ${{u}_{tt}}-{{\Delta }_{m}}u-\Delta u+g*\Delta u-{{\mu }_{1}}\Delta {{u}_{t}}\left( x, t \right)-{{\mu }_{2}}\Delta {{u}_{t}}\left( x, t-\tau \right)={{\left| u \right|}^{p-2}}u$ 解的爆破:当初始能量0 < E(0) < E1时, 利用能量函数构造凹函数L1(t), 得到微分不等式$\frac{\text{d}{{L}_{1}}\left( t \right)}{\text{d}t}\ge {{\xi }_{0}}L_{1}^{1+\nu }\left( t \right)\ \left( {{\xi }_{0}}>0, \nu >0, t\ge 0 \right)$, 在(0, t)上对此微分不等式积分, 从而可知存在有限时间T*>0, 使得当时间t趋于T*时, 该m-Laplacian型波方程的解爆破; 当初始能量E(0) < 0时, 构造凹函数L2(t), 通过同样的方法得到该方程的解存在有限时间爆破.
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出版历程
  • 收稿日期:  2020-08-04
  • 网络出版日期:  2021-03-24
  • 刊出日期:  2021-02-25

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