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具有非线性记忆项的半线性Moore-Gibson-Thompson方程解的爆破研究

欧阳柏平 侯春娟

欧阳柏平, 侯春娟. 具有非线性记忆项的半线性Moore-Gibson-Thompson方程解的爆破研究[J]. 华南师范大学学报(自然科学版), 2022, 54(2): 108-114. doi: 10.6054/j.jscnun.2022033
引用本文: 欧阳柏平, 侯春娟. 具有非线性记忆项的半线性Moore-Gibson-Thompson方程解的爆破研究[J]. 华南师范大学学报(自然科学版), 2022, 54(2): 108-114. doi: 10.6054/j.jscnun.2022033
OUYANG Baiping, HOU Chunjuan. On the Blow-up of Solutions to the Semilinear Moore-Gibson-Thompson Equation with a Nonlinear Memory Term[J]. Journal of South China normal University (Natural Science Edition), 2022, 54(2): 108-114. doi: 10.6054/j.jscnun.2022033
Citation: OUYANG Baiping, HOU Chunjuan. On the Blow-up of Solutions to the Semilinear Moore-Gibson-Thompson Equation with a Nonlinear Memory Term[J]. Journal of South China normal University (Natural Science Edition), 2022, 54(2): 108-114. doi: 10.6054/j.jscnun.2022033

具有非线性记忆项的半线性Moore-Gibson-Thompson方程解的爆破研究

doi: 10.6054/j.jscnun.2022033
基金项目: 

广东省基础与应用基础研究基金省市联合基金项目 2021A1515111048

广东省普通高校重点项目(自然科学) 2019KZDXM042

广州华商学院校内项目 2020HSDS01

详细信息
    通讯作者:

    欧阳柏平,Email: oytengfei79@tom.com

  • 中图分类号: O175.4

On the Blow-up of Solutions to the Semilinear Moore-Gibson-Thompson Equation with a Nonlinear Memory Term

  • 摘要: 为了探讨记忆项对高阶波动方程爆破解的非局部影响,研究了具有非线性记忆项的半线性Moore-Gibson-Thompson方程解的爆破问题:在次临界情况下,通过引入时变泛函,利用测试函数推出了该泛函的第一下界和下界序列。然后应用迭代和切片技巧证明了解的全局非存在性和生命跨度上界估计。
  • [1] CHEN W H, PALMIERIA. Nonexistence of global solutions for the semilinear Moore-Gibson-Thompson equation in the conservative case[J]. Discrete and Continuous Dynamical Systems, 2020, 40(9): 5513-5540. doi: 10.3934/dcds.2020236
    [2] CHEN W H, PALMIERI A. Blow-up result for a semili-near wave equation with a nonlinear memory term[M]//CICOGNANI M, SANTO D, PARMEGGIANI A, et al. An-omalies in Partial Differential Equations. Switzerland: Sp-ringer, 2021: 77-97.
    [3] CAIXETA A H, LASIECKA I, DOMINGOS CAVALCANTI V N. On long time behavior of Moore-Gibson-Thompson equation with molecular relaxation[J]. Evolution Equations & Control Theory, 2017, 5(4): 661-676.
    [4] LASIECKA I, WANG X J. Moore-Gibson-Thompson equation with memory, part I: exponential decay of energy[J]. Zeitschrift für angewandte Mathematik und Physik, 2016, 67(2): 17-39. doi: 10.1007/s00033-015-0597-8
    [5] PELLICER M, SAID-HOUARI B. Wellposedness and decay rates for the Cauchy problem of the Moore-Gibson-Thompson equation arising in high intensity ultrasound[J]. Applied Mathematics and Optimization, 2019, 80(2): 447-478. doi: 10.1007/s00245-017-9471-8
    [6] CHEN W H. Interplay effects on blow-up of weakly coupled systems for semilinear wave equations with general nonlinear memory terms[J]. Nonlinear Analysis, 2021, 202: 112160-112186. doi: 10.1016/j.na.2020.112160
    [7] CHEN W H, PALMIERI A. Weakly coupled system of semilinear wave equations with distinct scale-invariantterms in the linear part[J]. Zeitschrift für angewandte Mathematik und Physik, 2019, 70(2): 67-85. doi: 10.1007/s00033-019-1112-4
    [8] LAI N A, TAKAMURA H. Nonexistence of global solutions of nonlinear wave equations with weak time-dependent damping related to Glassey's conjecture[J]. Differential and Integral Equations, 2019, 32(1/2): 37-48.
    [9] OUYANG B P, LIN Y W. Nonexistence of global solutions for a semilinear double-wave equation with nonlinearity of derivative type[J]. Chinese Quarterly Journal of Mathe-matics, 2021, 36(2): 149-159.
    [10] PALMIERI A, TAKAMURA H. Nonexistence of global solutions for a weakly coupled system of semilinear damped wave equations in the scattering case with mixed nonli-near terms[J]. Nonlinear Differential Equations and Applications NoDEA, 2020, 27(6): 58-86. doi: 10.1007/s00030-020-00662-8
    [11] YORDANOV B T, ZHANG Q S. Finite time blow up for critical wave equations in high dimensions[J]. Journal of Functional Analysis, 2006, 231(2): 361-374.
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  • 被引次数: 0
出版历程
  • 收稿日期:  2021-04-28
  • 网络出版日期:  2022-05-12
  • 刊出日期:  2022-04-25

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