### Abstract

We study the initial value problem for a semi-linear dissipative plate equation in n-dimensional space. We observe that the dissipative structure of the linearized equation is of the regularity-loss type. This means that we have the optimal decay estimates of solutions under the additional regularity assumption on the initial data. This regularity-loss property causes the difficulty in solving the nonlinear problem. For our semi-linear problem, this difficulty can be overcome by introducing a set of time-weighted Sobolev spaces, where the time-weights and the regularity of the Sobolev spaces are determined by our regularity-loss property. Consequently, under smallness condition on the initial data, we prove the global existence and optimal decay of the solution in the corresponding Sobolev spaces.

Original language | English |
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Pages (from-to) | 471-501 |

Number of pages | 31 |

Journal | Journal of Hyperbolic Differential Equations |

Volume | 7 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2010 Sep 1 |

Externally published | Yes |

### Keywords

- Dissipative plate equation
- decay estimates
- global existence
- regularity-loss property

### ASJC Scopus subject areas

- Analysis
- Mathematics(all)