{"created":"2023-06-20T12:59:55.346387+00:00","id":3995,"links":{},"metadata":{"_buckets":{"deposit":"bce8cd66-d027-4a80-a78c-46fa3bd09a84"},"_deposit":{"created_by":2,"id":"3995","owners":[2],"pid":{"revision_id":0,"type":"depid","value":"3995"},"status":"published"},"_oai":{"id":"oai:fun.repo.nii.ac.jp:00003995","sets":["22:28","25:81:100"]},"author_link":["7196","7195","35"],"item_5_biblio_info_5":{"attribute_name":"書誌情報","attribute_value_mlt":[{"bibliographicIssueDates":{"bibliographicIssueDate":"2000","bibliographicIssueDateType":"Issued"},"bibliographicPageEnd":"133","bibliographicPageStart":"87","bibliographicVolumeNumber":"167","bibliographic_titles":[{"bibliographic_title":"Critical curve for p-q systems of nonlinear wave equations in three space dimensions"}]}]},"item_5_description_3":{"attribute_name":"抄録","attribute_value_mlt":[{"subitem_description":"非線形性が個々の成分によって違う波動方程式系は単独方程式では起き得なかった現象を生んでいる。それは例えば２成分の方程式系の場合で非線形性を２次元平面に描いたとき、時間大域古典解の存在と非存在を分離する臨界曲線が無限の長さを持つことである。この事実自身は前から知られていたが、非存在領域における解の最大存在時間の評価は全く成されていなかった。本論文では空間３次元において技術的な困難を次のように解決し、ゼロ解の最適安定性精密かつ完全に証明した。まず下からの評価である存在定理では、解の台をホイヘンスの原理によって線形部分の影響がある領域と無い領域に分け、それぞれで付随する積分方程式系の解のアプリオリ評価を導き逐次代入法で解を構成した。ここでの本質は領域の最適な分離である。一方上からの評価である非存在定理において一番解析が困難な臨界曲線上では、爆発領域を細かくスライスすることによって逐次代入における解の対数的増大を表現可能にした。この手法は単独方程式についても適用でき、今まで臨界値とそうでない場合の全く異なる証明法を統一することもできる。\n問題設定と存在定理、非存在定理の証明は高村が行い、アプリオリ評価は上見、黒川、高村が共同で行った。","subitem_description_type":"Abstract"}]},"item_5_description_4":{"attribute_name":"内容記述","attribute_value_mlt":[{"subitem_description":"学術論文","subitem_description_type":"Other"}]},"item_5_select_10":{"attribute_name":"単著共著","attribute_value_mlt":[{"subitem_select_item":"共著/joint"}]},"item_5_select_8":{"attribute_name":"査読有無","attribute_value_mlt":[{"subitem_select_item":"あり/yes"}]},"item_5_select_9":{"attribute_name":"研究業績種別","attribute_value_mlt":[{"subitem_select_item":"原著論文/Original Paper"}]},"item_access_right":{"attribute_name":"アクセス権","attribute_value_mlt":[{"subitem_access_right":"metadata only access","subitem_access_right_uri":"http://purl.org/coar/access_right/c_14cb"}]},"item_creator":{"attribute_name":"著者","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{"creatorName":"Agemi, Rentaro"}],"nameIdentifiers":[{"nameIdentifier":"7195","nameIdentifierScheme":"WEKO"}]},{"creatorNames":[{"creatorName":"Kurokawa, Yuki"}],"nameIdentifiers":[{"nameIdentifier":"7196","nameIdentifierScheme":"WEKO"}]},{"creatorNames":[{"creatorName":"Takamura, Hiroyuki"}],"nameIdentifiers":[{"nameIdentifier":"35","nameIdentifierScheme":"WEKO"},{"nameIdentifier":"40241781","nameIdentifierScheme":"e-Rad","nameIdentifierURI":"https://kaken.nii.ac.jp/ja/search/?qm=40241781"}]}]},"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":"Critical curve for p-q systems of nonlinear wave equations in three space dimensions","item_titles":{"attribute_name":"タイトル","attribute_value_mlt":[{"subitem_title":"Critical curve for p-q systems of nonlinear wave equations in three space dimensions"}]},"item_type_id":"5","owner":"2","path":["28","100"],"pubdate":{"attribute_name":"公開日","attribute_value":"2010-11-26"},"publish_date":"2010-11-26","publish_status":"0","recid":"3995","relation_version_is_last":true,"title":["Critical curve for p-q systems of nonlinear wave equations in three space dimensions"],"weko_creator_id":"2","weko_shared_id":-1},"updated":"2023-06-20T13:32:42.396021+00:00"}