Singular perturbations of the Kirchhoff string equation

The singular perturbations of the Kirchoff string equation were presented. A general case was proved by taking into account the perturbations of the Kirchhoff string with fractional powers of the Laplace operator and the convergence was proved in fractional Sobolev spaces of order greater or equal than 3/2. Results showed that the one space derivative with respect to initial data was natural and also occurred in the linear case.