The author proves that for initial data in a set S ? (H2(?) ∩ H0(?)) × H0(?), 1 1 unbounded in H0(?) × L2(?), the solut...The author proves that for initial data in a set S ? (H2(?) ∩ H0(?)) × H0(?), 1 1 unbounded in H0(?) × L2(?), the solutions of the Cauchy-Dirichlet problem for the 1 dissipative Kirchho? equation Z ?t u ? ν + L 2 | x u|2dx xu + δ?tu = 0 (x ∈ ?, t > 0), ? are global in [0,+∞) 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.展开更多
基金the Funds of the "Italian Ministero della Universit`a e della Ricerca Scientifica eTecnologica"
文摘The author proves that for initial data in a set S ? (H2(?) ∩ H0(?)) × H0(?), 1 1 unbounded in H0(?) × L2(?), the solutions of the Cauchy-Dirichlet problem for the 1 dissipative Kirchho? equation Z ?t u ? ν + L 2 | x u|2dx xu + δ?tu = 0 (x ∈ ?, t > 0), ? are global in [0,+∞) 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.
