Energy method in the partial Fourier space and application to stability problems in the half space

Yoshihiro Ueda*, Tohru Nakamura, Shuichi Kawashima

*この研究の対応する著者

研究成果: Article査読

3 被引用数 (Scopus)

抄録

The energy method in the Fourier space is useful in deriving the decay estimates for problems in the whole space Rn. In this paper, we study half space problems in R+n=R+×Rn-1 and develop the energy method in the partial Fourier space obtained by taking the Fourier transform with respect to the tangential variable x'∈Rn-1. For the variable x1∈R+ in the normal direction, we use L2 space or weighted L2 space. We apply this energy method to the half space problem for damped wave equations with a nonlinear convection term and prove the asymptotic stability of planar stationary waves by showing a sharp convergence rate for t→∞. The result obtained in this paper is a refinement of the previous one in Ueda et al. (2008) [13].

本文言語English
ページ(範囲)1169-1199
ページ数31
ジャーナルJournal of Differential Equations
250
2
DOI
出版ステータスPublished - 2011 1 15
外部発表はい

ASJC Scopus subject areas

  • 分析
  • 応用数学

フィンガープリント

「Energy method in the partial Fourier space and application to stability problems in the half space」の研究トピックを掘り下げます。これらがまとまってユニークなフィンガープリントを構成します。

引用スタイル