NOTE ON LOWER BOUNDS OF ENERGY GROWTH FOR SOLUTIONS TO WAVE EQUATIONS

Doi, Shin-ichi; Nishitani, Tatsuo; Ueda, Hideo

doi:https://doi.org/10.18910/23423

このアイテムのアクセス数:66件（2022-10-02 12:59 集計）

このアイテムへのリンクには次のURLをご利用ください: https://doi.org/10.18910/23423

このアイテムへのリンクには次のURLをご利用ください: https://hdl.handle.net/11094/23423

閲覧可能ファイル

ファイル	フォーマット	サイズ	閲覧回数	利用開始日	説明
ojm49_04_1065	pdf	285 KB	44	2013.01.25

論文情報

タイトル	NOTE ON LOWER BOUNDS OF ENERGY GROWTH FOR SOLUTIONS TO WAVE EQUATIONS
著者	NRID 1000000243006 1000000243006 著者名 Doi, Shin-ichi
	NRID 1000080127117 1000080127117 著者名 Nishitani, Tatsuo
	著者名 Ueda, Hideo
抄録	In this note we study lower bounds of energy growth for solutions to wave equations which are compact in space perturbations of the wave equation ∂^2_tu−Δu=0. Assuming that there exists a null bicharacteristic (x(t),ξ(t)), parametrized by the time t, such that x(t) remains inside a ball and ξ(t) outside a ball for t≥0 we prove that the solution operator R(t) is bounded from below by constant times √<｜ξ(t)｜/｜ξ(0)｜> in the operator norm. We apply this result to examples constructed by the same idea as in Colombini and Rauch [1] and show that there exist compact in space perturbations which cause exp(ct^α) growth of the energy for any given 0≤α≤1.
出版者	Osaka University and Osaka City University, Departments of Mathematics
収録物名	Osaka Journal of Mathematics
巻	49
号	4
開始ページ	1065
終了ページ	1085
刊行年月	2012-12
言語	英語
ハンドルURL	https://hdl.handle.net/11094/23423
DOI	https://doi.org/10.18910/23423
ISSN	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
カテゴリ	Osaka Journal of Mathematics / Volume 49, Number 4　(2012-12）

資源タイプ	紀要論文
ローカル資源タイプ	紀要論文
DCMI資源タイプ	text
DCTERMS.bibliographicCitation	Osaka Journal of Mathematics.49(4) p.1065-p.1085
DC.title	NOTE ON LOWER BOUNDS OF ENERGY GROWTH FOR SOLUTIONS TO WAVE EQUATIONS
DC.creator	Doi, Shin-ichi
	Nishitani, Tatsuo
	Ueda, Hideo
DC.publisher	Osaka University and Osaka City University, Departments of Mathematics
DC.language' scheme='DCTERMS.RFC1766	英語
DC.type' scheme='DCTERMS.DCMIType	text
DCTERMS.issued' scheme='DCTERMS.W3CDTF	2012-12
DCTERMS.abstract	In this note we study lower bounds of energy growth for solutions to wave equations which are compact in space perturbations of the wave equation ∂^2_tu−Δu=0. Assuming that there exists a null bicharacteristic (x(t),ξ(t)), parametrized by the time t, such that x(t) remains inside a ball and ξ(t) outside a ball for t≥0 we prove that the solution operator R(t) is bounded from below by constant times √<｜ξ(t)｜/｜ξ(0)｜> in the operator norm. We apply this result to examples constructed by the same idea as in Colombini and Rauch [1] and show that there exist compact in space perturbations which cause exp(ct^α) growth of the energy for any given 0≤α≤1.
DC.identifier	10.18910/23423
DC.format	application/pdf
citation_doi	https://doi.org/10.18910/23423
citation_title	NOTE ON LOWER BOUNDS OF ENERGY GROWTH FOR SOLUTIONS TO WAVE EQUATIONS
citation_author	Doi, Shin-ichi
	Nishitani, Tatsuo
	Ueda, Hideo
citation_publisher	Osaka University and Osaka City University, Departments of Mathematics
citation_language	英語
citation_date	2012-12
citation_journal_title	Osaka Journal of Mathematics
citation_volume	49
citation_issue	4
citation_firstpage	1065
citation_lastpage	1085
citation_issn	00306126
citation_public_url	https://hdl.handle.net/11094/23423
citation_doi_detail	10.18910/23423

閲覧可能ファイル

論文情報

論文詳細を表示