Abstract
AbstractIn this work, we investigate blowup phenomena for nonlinearly damped viscoelastic equations with logarithmic source effect and time delay in the velocity. Owing to the nonlinear damping term instead of strong or linear dissipation, we cannot apply the concavity method introduced by Levine. Thus, utilizing the energy method, we show that the solutions with not only non-positive initial energy but also some positive initial energy blow up at a finite point in time.
Funder
National Research Foundation of Korea
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Algebra and Number Theory,Analysis
Reference19 articles.
1. Barrow, J., Parsons, P.: Inflationary models with logarithmic potentials. Phys. Rev. D 52, 5576–5587 (1995)
2. Cao, Y., Liu, C.: Initial boundary value problem for a mixed pseudo-parabolic p-Laplacian type equation with logarithmic nonlinearity. Electron. J. Differ. Equ. 2018, Article ID 116 (2018)
3. Datko, R.: Not all feedback stabilized hyperbolic systems are robust with respect to small time delays in their feedbacks. SIAM J. Control Optim. 26, 697–713 (1988)
4. Di, H., Shang, Y., Song, Z.: Initial boundary value problems for a class of strongly damped semilinear wave equations with logarithmic nonlinearity. Nonlinear Anal., Real World Appl. 51, 102968 (2020)
5. Feng, B.: Global well-posedness and stability for a viscoelastic plate equation with a time delay. Math. Probl. Eng. 2015, Article ID 585021 (2015)
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