On a buffer phenomenon in the string interaction with a nonlinear oscillator (Q2761389)

The authors consider the boundary value problem NEWLINE\[NEWLINE \begin{gathered} u_{tt}+\varepsilon u_t = u_{xx},\\ u|_{x=0} = 0,\quad [u_{tt}+\varepsilon\alpha(u^2-1)u_t+\beta u]|_{x=1} = -\gamma u_x|_{x=1}, \end{gathered} NEWLINE\]NEWLINE where \(0<\varepsilon\ll 1\), \(\alpha,\beta,\gamma>0\), modelling the string interaction with a nonlinear oscillator. It is shown that any fixed number of stable and periodic solutions in \(t\) exists under appropriate choice of the parameters values.