Existence and general decay of solution for nonlinear viscoelastic two-dimensional beam with a nonlinear delay

被引：0
作者：
Billal Lekdim
Ammar Khemmoudj
机构：
[1] University Ziane Achour of Djelfa,Department of Mathematics
[2] University of Science and Technology Houari Boumediene,Laboratory of SDG, Faculty of Mathematics
来源：
Ricerche di Matematica | 2024年 / 73卷
关键词：
Nonlinear vibrations; General decay; Kelvin Voigt damping; Faedo–Galerkin method; Nonlinear delay term; 35B40; 35L05; 35G61;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We investigate the longitudinal and transversal vibrations of the viscoelastic beam with nonlinear tension and nonlinear delay term under the general decay rate for relaxation function. The existence theorem is proved by the Faedo–Galerkin method and using suitable Lyapunov functional to establish the general decay result.
引用
收藏
页码：261 / 282
页数：21
相关论文
共 55 条
  • [1] Aili M(2019)General decay of energy for a viscoelastic wave equation with a distributed delay term in the nonlinear internal dambing Rendiconti del Circolo Matematico di Palermo Series 2 1-21
  • [2] Khemmoudj A(1963)Global existence and energy decay of solutions to a nonlinear timoshenko beam system with a delay term Analyse mathematique-un theoreme de compacite 256 5042-1437
  • [3] Aubin JP(2014)Global existence and energy decay of solutions to a viscoelastic wave equation with a delay term in the non-linear internal feedback Taiw. J. Math. 18 1411-26
  • [4] Benaissa A(2014)Foundations of linear viscoelasticity Int. J. Dyn. Syst. Differ. Equ. 5 1-903
  • [5] Bahlil M(1961)Global existence and exponential decay of the solution for a viscoelastic wave equation with a delay Rev. Modern Phys. 33 239-2660
  • [6] Benaissa A(2014)Global existence and energy decay of solutions to a viscoelastic timoshenko beam system with a nonlinear delay term Zeitschrift für angewandte Mathematik und Physik 65 885-791
  • [7] Benguessoum A(2016)Boundary control of transverse motion of marine risers with actuator dynamics Appl. Anal. 95 2637-10
  • [8] Messaoudi SA(2008)Global well-posedness and stability for a viscoelastic plate equation with a time delay J. Sound Vib. 318 768-223
  • [9] Coleman BD(2015)General decay for a viscoelastic wave equation with density and time delay term in Math. Probl. Eng. 2015 1-11910
  • [10] Noll W(2018)Optimal decay rate estimates of a nonlinear viscoelastic kirchhoff plate Taiw. J. Math. 22 205-2853
123456