{"created":"2021-03-01T07:21:09.760792+00:00","id":41683,"links":{},"metadata":{"_buckets":{"deposit":"6edb0a63-7f14-4bff-bc27-f0ebfe552404"},"_deposit":{"id":"41683","owners":[],"pid":{"revision_id":0,"type":"depid","value":"41683"},"status":"published"},"_oai":{"id":"oai:tsukuba.repo.nii.ac.jp:00041683","sets":["117:5114","152:5654"]},"item_5_biblio_info_6":{"attribute_name":"書誌情報","attribute_value_mlt":[{"bibliographicIssueDates":{"bibliographicIssueDate":"2017-04","bibliographicIssueDateType":"Issued"},"bibliographicIssueNumber":"2","bibliographicPageEnd":"1001","bibliographicPageStart":"980","bibliographicVolumeNumber":"55","bibliographic_titles":[{"bibliographic_title":"SIAM journal on numerical analysis"}]}]},"item_5_creator_3":{"attribute_name":"著者別名","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{"creatorName":"高安, 亮紀"}],"nameIdentifiers":[{},{},{}]},{"creatorNames":[{"creatorName":"久保, 隆徹"}],"nameIdentifiers":[{},{},{}]}]},"item_5_description_4":{"attribute_name":"抄録","attribute_value_mlt":[{"subitem_description":"This paper presents a numerical method for verifying the existence and local uniqueness of a solution for an initial-boundary value problem of semilinear parabolic equations. The main theorem of this paper provides a sufficient condition for a unique solution to be enclosed within a neighborhood of a numerical solution. In the formulation used in this paper, the initial-boundary value problem is transformed into a fixed-point form using an analytic semigroup. The sufficient condition is derived from Banach's fixed-point theorem. This paper also introduces a recursive scheme to extend a time interval in which the validity of the solution can be verified. As an application of this method, the existence of a global-in-time solution is demonstrated for a certain semilinear parabolic equation.","subitem_description_type":"Abstract"}]},"item_5_publisher_27":{"attribute_name":"出版者","attribute_value_mlt":[{"subitem_publisher":"SIAM journal on numerical analysis"}]},"item_5_relation_11":{"attribute_name":"DOI","attribute_value_mlt":[{"subitem_relation_type_id":{"subitem_relation_type_id_text":"10.1137/141001664","subitem_relation_type_select":"DOI"}}]},"item_5_rights_12":{"attribute_name":"権利","attribute_value_mlt":[{"subitem_rights":"© 2017, Society for Industrial and Applied Mathematics"}]},"item_5_select_15":{"attribute_name":"著者版フラグ","attribute_value_mlt":[{"subitem_select_item":"publisher"}]},"item_5_source_id_7":{"attribute_name":"ISSN","attribute_value_mlt":[{"subitem_source_identifier":"0036-1429","subitem_source_identifier_type":"ISSN"}]},"item_5_source_id_9":{"attribute_name":"書誌レコードID","attribute_value_mlt":[{"subitem_source_identifier":"AA00831298","subitem_source_identifier_type":"NCID"}]},"item_creator":{"attribute_name":"著者","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{"creatorName":"Mizuguchi, Makoto"}],"nameIdentifiers":[{}]},{"creatorNames":[{"creatorName":"Takayasu, Akitoshi"}],"nameIdentifiers":[{}]},{"creatorNames":[{"creatorName":"Kubo, Takayuki"}],"nameIdentifiers":[{}]},{"creatorNames":[{"creatorName":"Oishi, Shin'ichi"}],"nameIdentifiers":[{}]}]},"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":"SIAM_JNA_55-2.pdf","filesize":[{"value":"451.4 kB"}],"format":"application/pdf","licensetype":"license_note","mimetype":"application/pdf","url":{"label":"SIAM_JNA_55-2","url":"https://tsukuba.repo.nii.ac.jp/record/41683/files/SIAM_JNA_55-2.pdf"},"version_id":"4cb73e19-1e60-47ed-a5ea-9237ce0979ea"}]},"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":"journal article","resourceuri":"http://purl.org/coar/resource_type/c_6501"}]},"item_title":"A Method of Verified Computations for Solutions to Semilinear Parabolic Equations Using Semigroup Theory","item_titles":{"attribute_name":"タイトル","attribute_value_mlt":[{"subitem_title":"A Method of Verified Computations for Solutions to Semilinear Parabolic Equations Using Semigroup Theory"}]},"item_type_id":"5","owner":"1","path":["5114","5654"],"pubdate":{"attribute_name":"公開日","attribute_value":"2017-06-27"},"publish_date":"2017-06-27","publish_status":"0","recid":"41683","relation_version_is_last":true,"title":["A Method of Verified Computations for Solutions to Semilinear Parabolic Equations Using Semigroup Theory"],"weko_creator_id":"1","weko_shared_id":5},"updated":"2022-04-27T09:12:36.393414+00:00"}