【摘 要】
：
The author proves that for initial data in a set S (H2(Ω) ∩ H10(Ω)) × H10(Ω),unbounded in H10(Ω) × L2(Ω), the solutions of the Cauchy-Dirichlet problem
【机 构】
：
Dipartimento di Matematica
【基金项目】
：
the Funds of the \"Italian Ministero della Università e della Ricerca Scientifica e Tecnologica\"
论文部分内容阅读
The author proves that for initial data in a set S (H2(Ω) ∩ H10(Ω)) × H10(Ω),unbounded in H10(Ω) × L2(Ω), the solutions of the Cauchy-Dirichlet problem for the dissipative Kirchhoff equationθ2u-(v+L∫Ω│▽xu│2dx)△xu+δθtu=0(xΩ,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.
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