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《山东大学学报(理学版)》 ›› 2025, Vol. 60 ›› Issue (2): 63-71.doi: 10.6040/j.issn.1671-9352.0.2023.278

• • 上一篇    

具黏弹性项的双曲方程解的存在性与衰减估计

范鑫宇,高艳超*   

  1. 长春理工大学数学与统计学院, 吉林 长春 130013
  • 发布日期:2025-02-14
  • 通讯作者: 高艳超(1983— ),男,副教授,博士,研究方向为偏微分方程. E-mail:ychaogao@163.com
  • 作者简介:范鑫宇(1999— ),女,硕士研究生,研究方向为偏微分方程. E-mail:fan_xinyu1007@163.com
  • 基金资助:
    吉林省自然科学基金资助项目(YDZJ202201ZYTS584)

Existence and decay estimation of solution for hyperbolic equation with viscoelastic term

FAN Xinyu, GAO Yanchao*   

  1. School of Mathematics and Statistics, Changchun University of Science and Technology, Changchun 130013, Jilin, China
  • Published:2025-02-14

摘要: 研究了一类具黏弹性项的四阶双曲方程的初边值问题。利用Galerkin方法得到了弱解的局部存在性,利用位势井方法证明了弱解的整体存在性,并给出了整体解的衰减估计。

关键词: 黏弹性项, 位势井, 四阶双曲方程, 衰减估计

Abstract: The initial boundary value problem of a class of fourth order hyperbolic equation with viscoelastic term is studied. The local existence of the weak solution is obtained by using Galerkin method. Then the global existence of the weak solution is proved using the potential well method, and the decay estimate of the global solution is given.

Key words: viscoelastic term, potential well, hyperbolic equation of fourth order, decay estimate

中图分类号: 

  • O175.27
[1] AL-GHARABLI M M, GUESMIA A, MESSAOUDI S A. Existence and a general decay results for a viscoelastic plate equation with a logarithmic nonlinearity[J]. Communications on Pure and Applied Analysis, 2019, 18(1):159-180.
[2] AL-GHARABLI M M. New general decay results for a viscoelastic plate equation with a logarithmic nonlinearity[J]. Boundary Value Problems, 2019, 2019(1):194-215.
[3] MERZOUG K, BOUMAZA N, GHERAIBIA B. General decay result of solutions for viscoelastic wave equation with logarithmic nonlinearity[C] //International Conference on Recent Advances in Mathematics and Informatics. Tebessa, Algeria: IEEE, 2021:1-4.
[4] LI Qian, HE Luofei. General decay and blow-up of solutions for a nonlinear viscoelastic wave equation with strong damping[J]. Boundary Value Problems, 2018, 2018(153):1-22.
[5] ZU Ge, GUO Bin. Bounds for lifespan of solutions to strongly damped semilinear wave equations with logarithmic sources and arbitrary initial energy[J]. Evolution Equations Control Theory, 2021, 10(2):259-270.
[6] YANG Hui, HAN Yuzhu. Blow-up for a damped p-Laplacian type wave equation with logarithmic nonlinearity[J]. Journal of Differential Equations, 2022, 306(1):569-589.
[7] AL-GHAREBLI M M, MESSAOUDI S A. The existence and the asymptotic behavior of a plate equation with frictional damping and a logarithmic source term[J]. Journal of Mathematical Analysis and Applications, 2017, 454(2):1114-1128.
[8] GROSS L. Logarithmic Sobolev inequalities[J]. American Journal of Mathematics, 1975, 97(4):1061-1083.
[9] CHEN H, LUO P, LIU G W. Global solution and blow-up of a semilinear heat equation with logarithmic nonlinearity[J]. Journal of Mathematical Analysis Applications, 2015, 422(1):84-98.
[10] SIMON J. Compact sets in the space Lp(0,T;B)[J]. Annali di Matematica pura ed Applicata, 1986, 1976(146):65-96.
[11] 伍卓群,李勇. 常微分方程[M]. 北京:高等教育出版社,2004. WU Zhuoqun, LI Yong. Ordinary differential equations[M]. Beijing: Higher Education Press, 2004.
[1] 张厚超, 朱维钧, 王俊俊. 非线性四阶双曲方程一个低阶混合元方法的超收敛和外推[J]. 山东大学学报(理学版), 2015, 50(12): 35-46.
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