Global existence theorem for non-homogeneous string with non-linear boundary condition

As a consequence of the global existence theorem for conservative scattering systems with non-linear feedback, the global existence theorem for non-homogeneous string with non-linear boundary condition at the left and is proved. The global solution is constructed in two stages: first, the evolution of the partial deivatives of the displacement of the string u(x,t) is recovered starting from the evolution of corresponding conservative scattering system and then the function u(x,t) is recovered starting from the evolution of these partial derivatives.