{"created":"2021-03-01T06:59:56.636758+00:00","id":40336,"links":{},"metadata":{"_buckets":{"deposit":"41bd2eb8-5e9f-40c9-baef-73bd908403ab"},"_deposit":{"id":"40336","owners":[],"pid":{"revision_id":0,"type":"depid","value":"40336"},"status":"published"},"_oai":{"id":"oai:repository.dl.itc.u-tokyo.ac.jp:00040336","sets":["312:6865:7055:7061","9:504:6868:7057:7062"]},"item_4_biblio_info_7":{"attribute_name":"書誌情報","attribute_value_mlt":[{"bibliographicIssueDates":{"bibliographicIssueDate":"1996","bibliographicIssueDateType":"Issued"},"bibliographicIssueNumber":"1","bibliographicPageEnd":"246","bibliographicPageStart":"199","bibliographicVolumeNumber":"3","bibliographic_titles":[{"bibliographic_title":"Journal of mathematical sciences, the University of Tokyo"}]}]},"item_4_description_13":{"attribute_name":"フォーマット","attribute_value_mlt":[{"subitem_description":"application/pdf","subitem_description_type":"Other"}]},"item_4_description_5":{"attribute_name":"抄録","attribute_value_mlt":[{"subitem_description":"We consider Cauchy problems for linear strictly hyperbolic equations of order $l$ with a small parameter $ε \\in (0, ε_0 ]$ : % \\begin{eqnarray} &\\{ &\\hspace{-3mm} (i ε )^{l-m} L (t,x,D_t , D_x; ε)+ M(t,x,D_t , D_x ;ε) \\} u(t,x; ε) \\\\ && =f(t,x;ε) \\\nonumber \\\\ &&\\mbox{for} (t,x) \\in (0,T) × \\mbox{\\boldmath $R$ }_x^d, \\\nonumber \\end{eqnarray} % \\begin{equation} D_t^j u(0,x; ε ) = g_j (x;ε) j=0,1,2, \\ldots, l-1 \\label{eqn: 0.2} \\end{equation} % where $L$ and $M$ are linear strictly hyperbolic operators of order $l$ and $m$ \\((l = m+1\\) or $m+2$) with $C^\\infty$ bounded derivatives with respect to \\((t,x,ε) \\in [0,\\infty) × \\mbox{\\boldmath $R$ }^d × [0,ε_0]\\). The aim of this paper is to give \\(C^{\\infty}\\) asymptotic expansions of solutions to singularly perturbed Cauchy problems of this type, when the characteristic roots of $L$ and $M$ satisfy the separation conditions. The points are to construct formal solutions (Proposition 5.3, 5.4), consisting of the regular part and the singular one (correction part of dispersive type) expressed by Maslov's canonical operators, and to give the error estimates in order to obtain asymptotic expansions with respect to $ε$ in the sense of arbitrarily higher order differentiability norms (Theorem 6.1, 6.2), when the supports of $f$ and $g_j$'s are contained in fixed compact sets.","subitem_description_type":"Abstract"}]},"item_4_publisher_20":{"attribute_name":"出版者","attribute_value_mlt":[{"subitem_publisher":"Graduate School of Mathematical Sciences, The University of Tokyo"}]},"item_4_source_id_10":{"attribute_name":"書誌レコードID","attribute_value_mlt":[{"subitem_source_identifier":"AA11021653","subitem_source_identifier_type":"NCID"}]},"item_4_source_id_8":{"attribute_name":"ISSN","attribute_value_mlt":[{"subitem_source_identifier":"13405705","subitem_source_identifier_type":"ISSN"}]},"item_4_subject_15":{"attribute_name":"日本十進分類法","attribute_value_mlt":[{"subitem_subject":"415","subitem_subject_scheme":"NDC"}]},"item_4_text_16":{"attribute_name":"Mathematical Reviews Number","attribute_value_mlt":[{"subitem_text_value":"MR1414625"}]},"item_4_text_17":{"attribute_name":"Mathmatical Subject Classification","attribute_value_mlt":[{"subitem_text_value":"35L30(MSC1991)"},{"subitem_text_value":"35B25(MSC1991)"},{"subitem_text_value":"35C20(MSC1991)"},{"subitem_text_value":"81Q20(MSC1991)"}]},"item_4_text_33":{"attribute_name":"原稿受領日","attribute_value_mlt":[{"subitem_text_value":"1994-04-11"}]},"item_creator":{"attribute_name":"著者","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{"creatorName":"Uchiyama, Koichi"}],"nameIdentifiers":[{"nameIdentifier":"138934","nameIdentifierScheme":"WEKO"}]}]},"item_files":{"attribute_name":"ファイル情報","attribute_type":"file","attribute_value_mlt":[{"accessrole":"open_date","date":[{"dateType":"Available","dateValue":"2017-06-27"}],"displaytype":"detail","filename":"jms030110.pdf","filesize":[{"value":"313.6 kB"}],"format":"application/pdf","licensetype":"license_note","mimetype":"application/pdf","url":{"label":"jms030110.pdf","url":"https://repository.dl.itc.u-tokyo.ac.jp/record/40336/files/jms030110.pdf"},"version_id":"904960da-b1b3-4fd0-ab3f-41b7a983e8e2"}]},"item_language":{"attribute_name":"言語","attribute_value_mlt":[{"subitem_language":"eng"}]},"item_resource_type":{"attribute_name":"資源タイプ","attribute_value_mlt":[{"resourcetype":"departmental bulletin paper","resourceuri":"http://purl.org/coar/resource_type/c_6501"}]},"item_title":"$L^2$-theory of singular perturbation of hyperbolic equations III Asymptotic expansions of dispersive type","item_titles":{"attribute_name":"タイトル","attribute_value_mlt":[{"subitem_title":"$L^2$-theory of singular perturbation of hyperbolic equations III Asymptotic expansions of dispersive type"}]},"item_type_id":"4","owner":"1","path":["7061","7062"],"pubdate":{"attribute_name":"公開日","attribute_value":"2008-03-04"},"publish_date":"2008-03-04","publish_status":"0","recid":"40336","relation_version_is_last":true,"title":["$L^2$-theory of singular perturbation of hyperbolic equations III Asymptotic expansions of dispersive type"],"weko_creator_id":"1","weko_shared_id":null},"updated":"2022-12-19T04:15:43.012045+00:00"}