Abstract
In this paper, we study an interconnected system of a Schrödinger and a wave equation with Kelvin-Voigt (K-V) damping, where the K-V damped wave equation performs as a dynamic feedback controller. We show that the system operator generates a C 0-semigroup of contractions in the energy state space, and the system is well-posed. By detailed spectral analysis, we know that the spectral of the system operator composes of two parts, point spectrum and continuous spectrum. Moreover, the points in the spectra all have negative real parts. It follows that the C 0-semigroup generated by the system operator achieves asymptotic stability.
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This work was supported by the National Natural Science Foundation of China.
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Lu, L., Wang, JM. (2016). Dynamic Boundary Stabilization of a Schrödinger Equation Through a Kelvin-Voigt Damped Wave Equation. In: Bélair, J., Frigaard, I., Kunze, H., Makarov, R., Melnik, R., Spiteri, R. (eds) Mathematical and Computational Approaches in Advancing Modern Science and Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-30379-6_12
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DOI: https://doi.org/10.1007/978-3-319-30379-6_12
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