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| SPECTRAL GAP SOLUTIONS OF THE DISSIPATIVE KIRCHHOFF EQUATION |
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Citation： |
S. PANIZZI.SPECTRAL GAP SOLUTIONS OF THE DISSIPATIVE KIRCHHOFF EQUATION[J].Chinese Annals of Mathematics B,2004,25(1):73~86 |
| Page view： 1218
Net amount： 763 |
Authors： |
S. PANIZZI; |
Foundation： |
Project supported by the Funds of the “Italian Ministero della Universita e della Ricerca Scientifica e
Tecnologica”. |
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| Abstract： |
The author proves that for initial data in a set $S \subset
(H^2(\Omega) \cap H^1_0(\Omega)) \times H^1_0(\Omega) $, unbounded
in $H^1_0(\Omega)\times L^2(\Omega)$,
the solutions of the Cauchy-Dirichlet problem for the dissipative
Kirchhoff equation
$$\partial_{t}^{2}u- \Big(\nu + L\g{
\int_{\p{\Omega}}}|\bigtriangledown_{x}u |^{2} dx \Big)
\bigtriangleup_{x}u + \delta \partial_{t} u= 0 \qquad (x\in \Omega
, \, t > 0),
$$
are global in $[0, +\infty)$ 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. |
Keywords： |
Spectral gap solutions, Dissipative Kirchhoff equation, Lacunae |
Classification： |
35L70, 35B40, 74H45 |
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