STABILIZATION OF TWO COUPLED ONE-DIMENSIONAL WAVE EQUATIONS BY A SINGLE DYNAMIC BOUNDARY CONTROL WITH DELAY

This paper investigates the stabilization of two coupled onedimensional wave equations on adjacent intervals \((a, b)\) and \((b, c)\), connected by a dissipative interface at \(x=b\). A single dynamic boundary control with time delay acts at the free end \(x=c\) of the second interval, while the first equation satisfies a Dirichlet condition at \(x=a\) and is coupled to the second at \(x=b\) through continuity and dissipative conditions. By introducing an auxiliary variable to reformulate the delay, we express the system as an abstract Cauchy problem in a suitable Hilbert space. Under suitable conditions on the damping parameters, specifically \(e_{0}>e_{1}\) and \(\tau e_{1}