{"created":"2023-07-27T06:59:58.777991+00:00","id":59745,"links":{},"metadata":{"_buckets":{"deposit":"565ea49d-71fc-475a-8741-ff7096eda5ec"},"_deposit":{"created_by":18,"id":"59745","owners":[18],"pid":{"revision_id":0,"type":"depid","value":"59745"},"status":"published"},"_oai":{"id":"oai:kanazawa-u.repo.nii.ac.jp:00059745","sets":["2812:2813:2835"]},"author_link":["80214","57"],"item_9_biblio_info_8":{"attribute_name":"書誌情報","attribute_value_mlt":[{"bibliographicIssueDates":{"bibliographicIssueDate":"1999-12-07","bibliographicIssueDateType":"Issued"},"bibliographicPageStart":"3p.","bibliographicVolumeNumber":"1997 – 1998","bibliographic_titles":[{"bibliographic_title":"平成10(1998)年度 科学研究費補助金 基盤研究(C) 研究成果報告書概要"},{"bibliographic_title":"1998 Fiscal Year Final Research Report Summary","bibliographic_titleLang":"en"}]}]},"item_9_creator_33":{"attribute_name":"著者別表示","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{}],"nameIdentifiers":[{},{}]}]},"item_9_description_21":{"attribute_name":"抄録","attribute_value_mlt":[{"subitem_description":"変分問題の中心課題の一つである自由境界問題の研究を行ってきた。視点としては、変分構造により、解の特異点等「定義域より低い次元の集合」をコントロールしている問題として統一的に捉えている。この特異集合の位置、正則性の理論の構築、数値解析プログラムの作成を行うことが目標であった。研究は補助金のおかげと、研究分担者の協力により、大きな進歩をみせた。\n変分汎関数の積分領域が動く自由境界問題では、非線形楕円型の場合で空間次元が2であるとき、自由境界の法線がヘルダー連続であることが示された。また、双曲型の時は、1次元の場合に、初期値と境界値にある種の関係が成り立てば、強い解(自由境界は2階連続微分可能)の構成を行うことができた。さらに、この数値解析法の開発も行い、高い精度が期待できる結果を得た。\nまた、低温超伝導のモデル方程式であるGinzburg-Landau方程式の数値解析法(楕円、放物、双曲型)の開発も行った。この問題は、vortexと称する渦状の高エネルギーの場所が生ずるのが特徴である。特に、波動方程式では、vortexが粒子のように運動するという結論を得た。我々の用いた手法は、液晶の数値解析にも使用可能である。\n以上の成果を、学術誌掲載(予定も含む)5報、国際会議議事録(レフェリー付き)2報、投稿中のプレプリント1報にまとめることができた。\n今後の課題として、より高次元の問題への対処、より特異性の高い問題への拡張、安定性の議論などの整備が考えられる。","subitem_description_type":"Abstract"},{"subitem_description":"We mainly investigated a free boundary problem related to a variational problem. Since our problem has a feature (hat the free boundary is a set of singular points of a minimizer and the energy concentrate on it. So, we can cosider that our purpose is on treating the energy concentration phenomena on the singularity of solutions. In this stand point of view, we treated the following type of problems :\n(1)Develop Regularity theory of elliptic free boundary problem related to minimizing functional with moving boundary,\n(2)Develop a Numerical method via a minimization process,\n(3)Develop a method related to solve a hyperbolic free boundary problem.\nFor problem (1), in 2-dimensional case, we successfully showed regularity of free boundary on some nonlinear case. For (2), we treated the Ginzburg-Landau functional which mainly appear in superconducting phenomema. In this, we developed a method due to discrete Morse semiflow for parabolic and hyperbolic problems. For (3), we constucted a strong solutions related to hyperbolic free boundary problems under some compatibility conditions. Moreover we developed a software to solve this with good accuracy. We summed up these results into 7 papers (appeared or in press) and I preprint (submitted).","subitem_description_type":"Abstract"}]},"item_9_description_22":{"attribute_name":"内容記述","attribute_value_mlt":[{"subitem_description":"研究課題/領域番号:09640170, 研究期間(年度):1997 – 1998","subitem_description_type":"Other"},{"subitem_description":"出典：研究課題「変分問題に関連する自由境界問題の数理解析 」課題番号09640170\n（KAKEN：科学研究費助成事業データベース（国立情報学研究所）） \n（https://kaken.nii.ac.jp/ja/report/KAKENHI-PROJECT-09640170/096401701998kenkyu_seika_hokoku_gaiyo/）を加工して作成","subitem_description_type":"Other"}]},"item_9_description_5":{"attribute_name":"提供者所属","attribute_value_mlt":[{"subitem_description":"金沢大学理学部","subitem_description_type":"Other"}]},"item_9_identifier_registration":{"attribute_name":"ID登録","attribute_value_mlt":[{"subitem_identifier_reg_text":"10.24517/00066000","subitem_identifier_reg_type":"JaLC"}]},"item_9_relation_28":{"attribute_name":"関連URI","attribute_value_mlt":[{"subitem_relation_name":[{"subitem_relation_name_text":"https://kaken.nii.ac.jp/search/?qm=20214223"}],"subitem_relation_type_id":{"subitem_relation_type_id_text":"https://kaken.nii.ac.jp/search/?qm=20214223","subitem_relation_type_select":"URI"}},{"subitem_relation_name":[{"subitem_relation_name_text":"https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-09640170/"}],"subitem_relation_type_id":{"subitem_relation_type_id_text":"https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-09640170/","subitem_relation_type_select":"URI"}},{"subitem_relation_name":[{"subitem_relation_name_text":"https://kaken.nii.ac.jp/ja/report/KAKENHI-PROJECT-09640170/096401701998kenkyu_seika_hokoku_gaiyo/"}],"subitem_relation_type_id":{"subitem_relation_type_id_text":"https://kaken.nii.ac.jp/ja/report/KAKENHI-PROJECT-09640170/096401701998kenkyu_seika_hokoku_gaiyo/","subitem_relation_type_select":"URI"}}]},"item_9_version_type_25":{"attribute_name":"著者版フラグ","attribute_value_mlt":[{"subitem_version_resource":"http://purl.org/coar/version/c_ab4af688f83e57aa","subitem_version_type":"AM"}]},"item_files":{"attribute_name":"ファイル情報","attribute_type":"file","attribute_value_mlt":[{"accessrole":"open_date","date":[{"dateType":"Available","dateValue":"2022-05-13"}],"displaytype":"detail","filename":"SC-PR-OMATA-S-kaken 1999-3p.pdf","filesize":[{"value":"106.7 kB"}],"format":"application/pdf","licensetype":"license_11","mimetype":"application/pdf","url":{"label":"SC-PR-OMATA-S-kaken 1999-3p.pdf","url":"https://kanazawa-u.repo.nii.ac.jp/record/59745/files/SC-PR-OMATA-S-kaken 1999-3p.pdf"},"version_id":"bf04a529-5f5f-477a-990e-31eb118d7039"}]},"item_language":{"attribute_name":"言語","attribute_value_mlt":[{"subitem_language":"jpn"}]},"item_resource_type":{"attribute_name":"資源タイプ","attribute_value_mlt":[{"resourcetype":"research report","resourceuri":"http://purl.org/coar/resource_type/c_18ws"}]},"item_title":"変分問題に関連する自由境界問題の数理解析","item_titles":{"attribute_name":"タイトル","attribute_value_mlt":[{"subitem_title":"変分問題に関連する自由境界問題の数理解析"},{"subitem_title":"Mathematical Analysis of free boundary problems related to a variational problem","subitem_title_language":"en"}]},"item_type_id":"9","owner":"18","path":["2835"],"pubdate":{"attribute_name":"公開日","attribute_value":"2022-05-13"},"publish_date":"2022-05-13","publish_status":"0","recid":"59745","relation_version_is_last":true,"title":["変分問題に関連する自由境界問題の数理解析"],"weko_creator_id":"18","weko_shared_id":-1},"updated":"2023-07-27T13:07:20.318238+00:00"}