论文标题
波动方程建模内存中的自由振动
Free vibrations in a wave equation modeling MEMS
论文作者
论文摘要
我们研究了在具有强度$λ$的静电电势的存在下作为膜（无粘性效应）的模型的非线性波方程。该膜在\ lbrack0，λ_{\ ast}] $的$λ\中具有唯一的稳定分支$u_λ$。我们证明，当参数$λ$变化时，分支$u_λ$具有无限数量的周期性解决方案（自由振动）分支。此外，使用功能设置，我们按数值计算分支$u_λ$及其定期解决方案分支。此方法对于在临界值$λ_{\ ast} $上严格验证稳定状态$u_λ$很有用。
We study a nonlinear wave equation appearing as a model for a membrane (without viscous effects) under the presence of an electrostatic potential with strength $λ$. The membrane has a unique stable branch of steady states $u_λ$ for $λ\in\lbrack0,λ_{\ast}]$. We prove that the branch $u_λ$ has an infinite number of branches of periodic solutions (free vibrations) bifurcating when the parameter $λ$ is varied. Furthermore, using a functional setting, we compute numerically the branch $u_λ$ and their branches of periodic solutions. This approach is useful to validate rigorously the steady states $u_λ$ at the critical value $λ_{\ast}$.
