Decay estimates of solutions to a semi-linear dissipative plate equation

Yousuke Sugitani, Shuichi Kawashima

研究成果: Contribution to journalArticle

42 引用 (Scopus)


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.

ジャーナルJournal of Hyperbolic Differential Equations
出版物ステータス出版済み - 9 1 2010

All Science Journal Classification (ASJC) codes

  • Analysis
  • Mathematics(all)

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