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

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

doi:info:doi/10.18910/23423

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タイトル	NOTE ON LOWER BOUNDS OF ENERGY GROWTH FOR SOLUTIONS TO WAVE EQUATIONS
著者	Doi, Shin-ichi Doi, Shin-ichi
	Nishitani, Tatsuo Nishitani, Tatsuo
	Ueda, Hideo 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.
公開者	Osaka University and Osaka City University, Departments of Mathematics
掲載誌名	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
ISSN	00306126
NCID	AA00765910
URL	http://hdl.handle.net/11094/23423
言語	英語
DOI	info:doi/10.18910/23423
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）

著者版フラグ	publisher
NII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
DCTERMS.issued" scheme="DCTERMS.W3CDTF	2012-12
DC.identifier" scheme="DCTERMS.URI	http://hdl.handle.net/11094/23423
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	info:doi/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	http://hdl.handle.net/11094/23423
citation_doi	info:doi/10.18910/23423

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