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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. (English) Zbl 1436.35054

Summary: 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.

MSC:

35B44 Blow-up in context of PDEs
35L05 Wave equation
35L20 Initial-boundary value problems for second-order hyperbolic equations
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