Stabilizability for Quasilinear Klein–Gordon–Schrödinger System with Variable Coefficients

Weijia Li (), Yuqi Shangguan () and Weiping Yan ()
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Weijia Li: Guangxi University
Yuqi Shangguan: Guangxi University
Weiping Yan: Guangxi University

Journal of Optimization Theory and Applications, 2024, vol. 202, issue 2, No 8, 703-744

Abstract: Abstract This paper concerns with the stabilizability for a quasilinear Klein–Gordon–Schrödinger system with variable coefficients in dimensionless form. The stabilizability of quaslinear Klein–Gordon-Wave system with the Kelvin–Voigt damping has been considered by Liu–Yan–Zhang (SIAM J Control Optim 61:1651–1678, 2023). Our main contribution is to find a suitable linear feedback control law such that the quasilinear Klein–Gordon–Schrödinger system is exponentially stable under certain smallness conditions.

Keywords: Stabilizability; Kelvin–Voigt damping; Klein–Gordon–Schrödinger system; 93B52; 93D15; 81Q05 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10957-024-02445-y

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