Author:
Chen Shaohua,Xu Runzhang,Yang Chao
Abstract
We propose a new differential inequality that improve the upper bound of the blowup time estimate for nonlinear fourth-order damped wave equations with strain term and arbitrary positive initial energy. We also give two new initial conditions to expand the range of the initial data leading to the finite time blowup of solutions. We obtain a sharp result of finite time blowup for the special case of the new differential inequality.We illustrate our results with some simulations.
Reference15 articles.
1. L. J. An, A. Peirce; A weakly nonlinear analysis of elasto-plastic-microstructure models, SIAM J. Appl. Math., 55 (1995), 136-155.
2. L. H. Fatori, M. A. Jorge Silva, T. F. Ma, Z. J. Yang; Long-time behavior of a class of thermoelastic plates with nonlinear strain, J. Differential Equations, 259 (2015), 4831-4862.
3. J. Han, R. Z. Xu, Y. B. Yang; Asymptotic behavior and finite time blow up for damped fourth order nonlinear evolution equation, Asymptotic. Anal., 1 (2020), 1-21.
4. M. O. Korpusov; Non-existence of global solutions to generalized dissipative Klein-Gordon equations with positive energy, Electron. J. Differential Equations, 2012 (2012) no. 119, 1-10.
5. Y. C. Liu, R. Z. Xu; A class of fourth order wave equations with dissipative and nonlinear strain terms, J. Differential Equations, 244 (2008), 200-228.