{"created":"2021-03-01T06:36:43.860216+00:00","id":28625,"links":{},"metadata":{"_buckets":{"deposit":"817f1284-2009-4249-a9ec-131b30efb717"},"_deposit":{"id":"28625","owners":[],"pid":{"revision_id":0,"type":"depid","value":"28625"},"status":"published"},"_oai":{"id":"oai:nagoya.repo.nii.ac.jp:00028625","sets":["312:313:314"]},"author_link":["93737","93738"],"item_10_biblio_info_6":{"attribute_name":"書誌情報","attribute_value_mlt":[{"bibliographicIssueDates":{"bibliographicIssueDate":"2019","bibliographicIssueDateType":"Issued"},"bibliographicIssueNumber":"4","bibliographicPageEnd":"824","bibliographicPageStart":"785","bibliographicVolumeNumber":"8","bibliographic_titles":[{"bibliographic_title":"Evolution Equations & Control Theory","bibliographic_titleLang":"en"}]}]},"item_10_description_4":{"attribute_name":"抄録","attribute_value_mlt":[{"subitem_description":"The solution to a free boundary problem of Bernoulli type, also known as Alt-Caffarelli problem, is studied via shape optimization techniques. In particular, a novel energy-gap cost functional approach with a state constraint consisting of a Robin condition is proposed as a shape optimization reformulation of the problem. Accordingly, the shape derivative of the cost is explicitly determined, and using the gradient information, a Lagrangian-like method is used to formulate an efficient boundary variation algorithm to numerically solve the minimization problem. The second order shape derivative of the cost is also computed, and through its characterization at the solution of the Bernoulli problem, the ill-posedness of the shape optimization formulation is proved. The analysis of the proposed formulation is completed by addressing the existence of optimal solution of the shape optimization problem and is accomplished by proving the continuity of the solution of the state problems with respect to the domain. The feasibility of the newly proposed method and its comparison with the classical energy-gap type cost functional approach is then presented through various numerical results. The numerical exploration issued in the study also includes results from a second-order optimization procedure based on a Newton-type method for resolving such minimization problem. This computational scheme put forward in the paper utilizes the Hessian information at the optimal solution and thus offers a state-of-the-art numerical approach for solving such free boundary problem via shape optimization setting.","subitem_description_language":"en","subitem_description_type":"Abstract"}]},"item_10_description_5":{"attribute_name":"内容記述","attribute_value_mlt":[{"subitem_description":"Online Published: 2019-06-28 ファイル公開：2020-06-28","subitem_description_language":"ja","subitem_description_type":"Other"}]},"item_10_publisher_32":{"attribute_name":"出版者","attribute_value_mlt":[{"subitem_publisher":"American Institute of Mathematical Sciences","subitem_publisher_language":"en"}]},"item_10_relation_11":{"attribute_name":"DOI","attribute_value_mlt":[{"subitem_relation_type":"isVersionOf","subitem_relation_type_id":{"subitem_relation_type_id_text":"https://doi.org/10.3934/eect.2019038","subitem_relation_type_select":"DOI"}}]},"item_10_rights_12":{"attribute_name":"権利","attribute_value_mlt":[{"subitem_rights":"This is a pre-copy-editing, author-produced PDF of an article accepted for publication in [Evolution Equations & Control Theory] following peer review. The definitive publisher-authenticated version [A new energy-gap cost functional approach for the exterior Bernoulli free boundary problem, Evolution Equations & Control Theory, 8, 4, 785-824, 2019-6-28, Julius Fergy T. Rabago, Hideyuki Azegami] is available online at: https://doi.org/10.3934/eect.2019038.","subitem_rights_language":"en"}]},"item_10_select_15":{"attribute_name":"著者版フラグ","attribute_value_mlt":[{"subitem_select_item":"author"}]},"item_10_source_id_62":{"attribute_name":"ISSN（Online）","attribute_value_mlt":[{"subitem_source_identifier":"2163-2480","subitem_source_identifier_type":"EISSN"}]},"item_1615787544753":{"attribute_name":"出版タイプ","attribute_value_mlt":[{"subitem_version_resource":"http://purl.org/coar/version/c_ab4af688f83e57aa","subitem_version_type":"AM"}]},"item_access_right":{"attribute_name":"アクセス権","attribute_value_mlt":[{"subitem_access_right":"open access","subitem_access_right_uri":"http://purl.org/coar/access_right/c_abf2"}]},"item_creator":{"attribute_name":"著者","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{"creatorName":"Fergy T. Rabago, Julius","creatorNameLang":"en"}],"nameIdentifiers":[{"nameIdentifier":"93737","nameIdentifierScheme":"WEKO"}]},{"creatorNames":[{"creatorName":"Azegami, Hideyuki","creatorNameLang":"en"}],"nameIdentifiers":[{"nameIdentifier":"93738","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":"2020-06-28"}],"displaytype":"detail","filename":"main.pdf","filesize":[{"value":"939.3 kB"}],"format":"application/pdf","licensetype":"license_note","mimetype":"application/pdf","url":{"label":"main","objectType":"fulltext","url":"https://nagoya.repo.nii.ac.jp/record/28625/files/main.pdf"},"version_id":"5fed0ac4-2515-4df1-8d12-86caeca115c4"}]},"item_keyword":{"attribute_name":"キーワード","attribute_value_mlt":[{"subitem_subject":"Shape optimization","subitem_subject_scheme":"Other"},{"subitem_subject":"shape derivative","subitem_subject_scheme":"Other"},{"subitem_subject":"Bernoulli problem","subitem_subject_scheme":"Other"},{"subitem_subject":"gradient method","subitem_subject_scheme":"Other"},{"subitem_subject":"Newton method","subitem_subject_scheme":"Other"}]},"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 new energy-gap cost functional approach for the exterior Bernoulli free boundary problem","item_titles":{"attribute_name":"タイトル","attribute_value_mlt":[{"subitem_title":"A new energy-gap cost functional approach for the exterior Bernoulli free boundary problem","subitem_title_language":"en"}]},"item_type_id":"10","owner":"1","path":["314"],"pubdate":{"attribute_name":"PubDate","attribute_value":"2019-10-16"},"publish_date":"2019-10-16","publish_status":"0","recid":"28625","relation_version_is_last":true,"title":["A new energy-gap cost functional approach for the exterior Bernoulli free boundary problem"],"weko_creator_id":"1","weko_shared_id":-1},"updated":"2023-01-16T04:21:32.201849+00:00"}