{"created":"2021-03-01T06:59:33.519952+00:00","id":39997,"links":{},"metadata":{"_buckets":{"deposit":"f211fef9-a4f8-45b4-9d88-9eca8b552285"},"_deposit":{"id":"39997","owners":[],"pid":{"revision_id":0,"type":"depid","value":"39997"},"status":"published"},"_oai":{"id":"oai:repository.dl.itc.u-tokyo.ac.jp:00039997","sets":["312:6865:6889:6893","9:504:6868:6891:6894"]},"item_4_biblio_info_7":{"attribute_name":"書誌情報","attribute_value_mlt":[{"bibliographicIssueDates":{"bibliographicIssueDate":"2014-01-15","bibliographicIssueDateType":"Issued"},"bibliographicIssueNumber":"3","bibliographicPageEnd":"433","bibliographicPageStart":"375","bibliographicVolumeNumber":"20","bibliographic_titles":[{"bibliographic_title":"Journal of mathematical sciences, the University of Tokyo"}]}]},"item_4_description_5":{"attribute_name":"抄録","attribute_value_mlt":[{"subitem_description":"We discuss the large time behavior of a weak solution of the Keller-Segel system of degenerate type: ∂tu − Δuα + div(u∇ψ) = 0, t>0, x ∈ Rn, − Δψ + ψ = u, t > 0, x ∈ Rn, u(0, x) = u0(x) ≥ 0, x∈ Rn, where α > 1. It is known when the exponent α = 2 − 2 / n, then the problem shows the critical situation. In this case, we show that the small data global solution decays and its asymptotic profile converges to the Barenblatt-Pattle solution U(t) = (1 + t)−n/σ (A − |x|2/(1 + t)1/σ)+1/(α−1)+ in L1 such as ||u(t)−U(t)||1 ≤ C(1 + t)−ν, where ν > 0 is depending on n and the regularity of the solution. To show this, we employ the forward self-similar transform and use the entropy dissipation term to derive the asymptotic profile due to Carrillo-Toscani [12] and Ogawa [47]. The Hölder continuity of the weak solution for the forward self-similar equation plays a crucial role. We derive the uniform Hölder continuity by using the rescaled alternative selection originated by DiBenedetto-Friedman [18, 19].","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":"MR"}]},"item_4_text_17":{"attribute_name":"Mathmatical Subject Classification","attribute_value_mlt":[{"subitem_text_value":"35B40(MSC2010)"},{"subitem_text_value":"35B65(MSC2010)"},{"subitem_text_value":"35K65(MSC2010)"}]},"item_4_text_33":{"attribute_name":"原稿受領日","attribute_value_mlt":[{"subitem_text_value":"2013-06-11"}]},"item_4_text_4":{"attribute_name":"著者所属","attribute_value_mlt":[{"subitem_text_value":"Department of Mathematics, College of Science and Technology, Nihon University"},{"subitem_text_value":"Mathematical Institute, Tohoku University"}]},"item_creator":{"attribute_name":"著者","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{"creatorName":"Mizuno, Masashi"}],"nameIdentifiers":[{"nameIdentifier":"92423","nameIdentifierScheme":"WEKO"}]},{"creatorNames":[{"creatorName":"Ogawa, Takayoshi"}],"nameIdentifiers":[{"nameIdentifier":"92424","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":"2017-06-14"}],"displaytype":"detail","filename":"jms200304.pdf","filesize":[{"value":"349.9 kB"}],"format":"application/pdf","licensetype":"license_note","mimetype":"application/pdf","url":{"label":"jms200304.pdf","url":"https://repository.dl.itc.u-tokyo.ac.jp/record/39997/files/jms200304.pdf"},"version_id":"ad9e6ef7-8ed0-40ad-8af0-a041529bb8b1"}]},"item_keyword":{"attribute_name":"キーワード","attribute_value_mlt":[{"subitem_subject":"Degenerate Keller-Segel system","subitem_subject_scheme":"Other"},{"subitem_subject":"Hölder regularity","subitem_subject_scheme":"Other"},{"subitem_subject":"uniform asymptotic estimates","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":"departmental bulletin paper","resourceuri":"http://purl.org/coar/resource_type/c_6501"}]},"item_title":"Regularity and Asymptotic Behavior for the Keller-Segel System of Degenerate Type with Critical Nonlinearity","item_titles":{"attribute_name":"タイトル","attribute_value_mlt":[{"subitem_title":"Regularity and Asymptotic Behavior for the Keller-Segel System of Degenerate Type with Critical Nonlinearity"}]},"item_type_id":"4","owner":"1","path":["6893","6894"],"pubdate":{"attribute_name":"公開日","attribute_value":"2015-12-15"},"publish_date":"2015-12-15","publish_status":"0","recid":"39997","relation_version_is_last":true,"title":["Regularity and Asymptotic Behavior for the Keller-Segel System of Degenerate Type with Critical Nonlinearity"],"weko_creator_id":"1","weko_shared_id":null},"updated":"2022-12-19T04:14:32.116808+00:00"}