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

Yousuke Sugitani, Shuichi Kawashima

Research output: Contribution to journalArticle

42 Citations (Scopus)

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 languageEnglish
Pages (from-to)471-501
Number of pages31
JournalJournal of Hyperbolic Differential Equations
Volume7
Issue number3
DOIs
Publication statusPublished - 2010 Sep 1
Externally publishedYes

Fingerprint

Plate Equation
Dissipative Equations
Decay Estimates
Semilinear
Regularity
Sobolev Spaces
Dissipative Structure
Weighted Sobolev Spaces
Global Existence
Initial Value Problem
Nonlinear Problem
n-dimensional
Decay

Keywords

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

ASJC Scopus subject areas

  • Analysis
  • Mathematics(all)

Cite this

Decay estimates of solutions to a semi-linear dissipative plate equation. / Sugitani, Yousuke; Kawashima, Shuichi.

In: Journal of Hyperbolic Differential Equations, Vol. 7, No. 3, 01.09.2010, p. 471-501.

Research output: Contribution to journalArticle

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