LARGE TIME BEHAVIOR OF GLOBAL SOLUTIONS TO NONLINEAR WAVE EQUATIONS WITH FRICTIONAL AND VISCOELASTIC DAMPING TERMS

Ikehata, Ryo; Takeda, Hiroshi

Osaka Journal of Mathematics, 2019, 56(4), 807-830

アクセス数:222件（2025-04-29 14:12 集計）

固定URL: https://doi.org/10.18910/73629

閲覧可能ファイル 

ファイル フォーマット 利用条件 サイズ 閲覧回数 利用開始日 説明 information
ojm56_04_807 pdf なし 189 KB 83 2019.11.27  

論文情報

ファイル出力 EndNote Basic出力 Mendeley出力

タイトル
LARGE TIME BEHAVIOR OF GLOBAL SOLUTIONS TO NONLINEAR WAVE EQUATIONS WITH FRICTIONAL AND VISCOELASTIC DAMPING TERMS
著者
NRID
1000010249758 1000010249758
著者名
Ikehata, Ryo
NRID
1000010589237 1000010589237
著者名
Takeda, Hiroshi
抄録
In this paper, we study the Cauchy problem for a nonlinear wave equation with frictional and viscoelastic damping terms in R＾n. As is pointed out by [10], in this combination, the frictional damping term is dominant for the viscoelastic one for the global dynamics of the linear equation. In this note we observe that if the initial data is small, the frictional damping term is again dominant even in the nonlinear equation case. In other words, our main result is diffusion phenomena: the solution is approximated by the heat kernel with a suitable constant. Especially, the result obtained for the n = 3 case is essentially new. Our proof is based on several estimates for the corresponding linear equations.
出版者
Osaka University and Osaka City University, Departments of Mathematics
収録物名
Osaka Journal of Mathematics
巻(号)
56(4)
ページ
807-830
刊行年月
2019-10
言語
英語
ハンドルURL
https://hdl.handle.net/11094/73629
DOI
https://doi.org/10.18910/73629
PISSN
00306126
NCID
AA00765910
アクセス権
open access
出版タイプ
Version of Record
カテゴリ
紀要論文 Departmental Bulletin Paper
Osaka Journal of Mathematics / Volume 56, Number 4 （2019-10）