数学
劈形算符
非线性系统
边值问题
班级(哲学)
期限(时间)
数学分析
能量(信号处理)
边界(拓扑)
数学物理
梁(结构)
组合数学
物理
欧米茄
量子力学
统计
人工智能
计算机科学
光学
作者
Gongwei Liu,Ming Yin,Suxia Xia
标识
DOI:10.1007/s00009-023-02469-0
摘要
In this paper, we investigate the initial boundary value problem of the following nonlinear extensible beam equation with nonlinear damping term $$\begin{aligned} u_{t t}+\Delta ^2 u-M\left( \Vert \nabla u\Vert ^2\right) \Delta u-\Delta u_t+\left| u_t\right| ^{r-1} u_t=|u|^{p-1} u \end{aligned}$$ which was considered by Yang et al. (Adv Nonlinear Stud 22:436–468, 2022). We consider the problem with the nonlinear damping and establish the finite time blow-up of the solution for the initial data at arbitrary high energy level, including the estimate lower and upper bounds of the blow-up time. The result provides some affirmative answer to the open problems given in Yang et al. (2022).
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