Boundedness and convergence of solutions for the string coupled to a   nonlinear oscillator
  A system of equations consisting of an infinite string coupled to a nonlinear oscillator is considered. The Cauchy problem for the system with the periodic initial data is studied. The main goal is to prove the convergence of the solutions as $t\to\infty$ to a time periodic solution. 
T.V. Dudnikova
math.AP math-ph math.MP