Decay property for a plate equation with memory-type dissipation

Yongqin Liu, Shuichi Kawashima

研究成果: Contribution to journalArticle査読

28 被引用数 (Scopus)

抄録

In this paper we focus on the initial value problem of the semilinear plate equation with memory in multi-dimensions (n > 1), the decay structure of which is of regularity-loss property. By using Fourier transform and Laplace transform, we obtain the fundamental solutions and thus the solution to the corresponding linear problem. Appealing to the point-wise estimate in the Fourier space of solutions to the linear problem, we get estimates and properties of solution operators, by exploiting which decay estimates of solutions to the linear problem are obtained. Also by introducing a set of time-weighted Sobolev spaces and using the contraction mapping theorem, we obtain the global in-time existence and the optimal decay estimates of solutions to the semi-linear problem under smallness assumption on the initial data.

本文言語英語
ページ(範囲)531-547
ページ数17
ジャーナルKinetic and Related Models
4
2
DOI
出版ステータス出版済み - 6 2011

All Science Journal Classification (ASJC) codes

  • 数値解析
  • モデリングとシミュレーション

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