Spectral gap solutions of the Kirchhoff equation

The author proves that for initial data in a set S subset of suitable Sobolev spaces, the solutions of the Cauchy-Dirichlet problem for the dissipative Kirchhoff are global in time and decay exponentially. The functions in S do not satisfy any additional regularity assumption, instead they must satisfy a condition relating their energy with the largest lacuna in their Fourier expansion. The larger is the lacuna the larger is the energy allowed