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Finite time blow-up for a wave equation with dynamic boundary condition at critical and high energy levels in control systems

Xiaoqiang Dai,Chao Yang,Shaobin Huang,Tao Yu,Yuanran Zhu

ELECTRONIC RESEARCH ARCHIVE（2020）

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Abstract
We study the initial boundary value problem of linear homogeneous wave equation with dynamic boundary condition. We aim to prove the finite time blow-up of the solution at critical energy level or high energy level with the nonlinear damping term on boundary in control systems.
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Key words
High energy level,critical energy level,dynamical boundary condition,wave equation
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