Stabilization of interaction of a string with two nonlinear oscillators (Q1851535)

The authors consider the system of equations \[ \begin{gathered} \mu\ddot u(x,t) = Tu''(x,t),\quad x\in \mathbb R\backslash Q,\\ m_i\ddot y_i(t) = F_i(y_i(t))+T[u'(x_i+0,t)-u'(x_i-0,t)],\quad i=1,2,\end{gathered} \] where \[ \mu,T>0,\;Q=\{x_1,x_2\},\;m_i>0,\;F_i: \mathbb R\to \mathbb R,\;y_i(t)\equiv u(x_i\pm 0,t),\;i=1,2. \] The system describes small transversal oscillations of a homogeneous infinite string connected at the points \(x_i\) with two oscillators with masses \(m_i\not=0\), \(i=1,2\). In the paper it is proved that the set of stationary points of the system is a point attractor.