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<p>In this paper, we address exponential stabilization of transmission problem of the wave equation with dynamical boundary conditions. We consider waves passing from a medium in which the speed is <i>a</i><sub>1</sub> into a medium in which the speed <i>a</i><sub>2</sub> in the case of total internal reflection and show that such a system can be controlled by introducing both dynamical boundary control along the exterior boundary and distributed control near the transmission boundary. We obtain that the system is exponential stabilization without any restriction on <i>a</i><sub>1</sub>, <i>a</i><sub>2</sub> and the transmission boundary.</p>

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Stabilization for the Problem of Transmission of Wave Equation with Dynamical Boundary Conditions

  • 期刊论文

  • 发表日期：

    2026年1月22日

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  • Zhi-ling Guo,
  • Shu-gen Chai

摘要

In this paper, we address exponential stabilization of transmission problem of the wave equation with dynamical boundary conditions. We consider waves passing from a medium in which the speed is a1 into a medium in which the speed a2 in the case of total internal reflection and show that such a system can be controlled by introducing both dynamical boundary control along the exterior boundary and distributed control near the transmission boundary. We obtain that the system is exponential stabilization without any restriction on a1, a2 and the transmission boundary.