Author:
Choucha Abdelbaki,Haiour Mohamed,Boulaaras Salah
Abstract
AbstractIn this work, we consider a quasilinear system of viscoelastic equations with dispersion, source, and variable exponents. Under suitable assumptions on the initial data and the relaxation functions, we obtained that the solution of the system is global and bounded. Next, the blow-up is proved with negative initial energy. After that, the exponential growth of solutions is showed with positive initial energy, and by using an integral inequality due to Komornik, the general decay result is obtained in the case of absence of the source term.
Publisher
Springer Science and Business Media LLC
Reference29 articles.
1. Agre, K., Rammaha, M.A.: Systems of nonlinear wave equations with damping and source terms. Differ. Integral Equ. 19, 1235–1270 (2007)
2. Al-Mahdi, A.: The coupling system of Kirchhoff and Euler-Bernoulli plates with logarithmic source terms: strong damping versus weak damping of variable-exponent type. AIMS Math. 8(11), 27439–27459 (2023). https://doi.org/10.3934/math.20231404
3. Ball, J.: Remarks on blow-up and nonexistence theorems for nonlinear evolutions equation. Q. J. Math. 28, 473–486 (1977)
4. Ben Aissa, A., Ouchenane, D., Zennir, K.: Blow up of positive initial-energy solutions to systems of nonlinear wave equations with degenerate damping and source terms. Nonlinear Stud. 19(4), 523–535 (2012)
5. Bland, D.R.: The Theory of Linear Viscoelasticity. Courier Dover Publications, Mineola (2016)
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献