Affiliation:
1. Office for Education Accreditation, Pusan National University, Keumjeong-gu 46241 , Busan , South Korea
Abstract
Abstract
In the present work, we establish a blow-up criterion for viscoelastic wave equations with nonlinear damping, logarithmic source, delay in the velocity, and acoustic boundary conditions. Due to the nonlinear damping term, we cannot apply the concavity method introduced by Levine. Thus, we use the energy method to show that the solution with negative initial energy blows up after finite time. Furthermore, we investigate the upper and lower bounds of the blow-up time.
Reference18 articles.
1. J. Barrow and P. Parsons, Inflationary models with logarithmic potentials, Phys. Rev. D 52 (1995), 5576–5587.
2. Y. Boukhatem and B. Benabderrahmane, Polynomial decay and blow up of solutions for variable coefficients viscoelastic wave equation with acoustic boundary conditions, Acta Math. Sinica 32 (2016), 153–174.
3. Y. Cao and C. Liu, Initial boundary value problem for a mixed pseudo-parabolic p-Laplacian type equation with logarithmic nonlinearity, Electron. J. Differential Equations 2018 (2018), 116, 19 pages.
4. H. Di, Y. Shang, and Z. Song, Initial boundary value problems for a class of strongly damped semilinear wave equations with logarithmic nonlinearity, Nonlinear Anal.: R.W.A. 51 (2020), 102968.
5. P. Gorka, Logarithmic Klein-Gordon equation, Acta Phys. Polon. B 40 (2009), 59–66.
Cited by
5 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