{"created":"2021-03-01T06:59:37.037787+00:00","id":40049,"links":{},"metadata":{"_buckets":{"deposit":"a2af046d-4b92-468e-8d44-bb0fc63529db"},"_deposit":{"id":"40049","owners":[],"pid":{"revision_id":0,"type":"depid","value":"40049"},"status":"published"},"_oai":{"id":"oai:repository.dl.itc.u-tokyo.ac.jp:00040049","sets":["312:6865:6919:6920","9:504:6868:6921:6922"]},"item_4_biblio_info_7":{"attribute_name":"書誌情報","attribute_value_mlt":[{"bibliographicIssueDates":{"bibliographicIssueDate":"2011-03-29","bibliographicIssueDateType":"Issued"},"bibliographicIssueNumber":"4","bibliographicPageEnd":"358","bibliographicPageStart":"323","bibliographicVolumeNumber":"17","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":"As a basic model, the Cauchy problem in RN×R+ for the 2mth-order semilinear parabolic equation of the diffusion-absorp\\-tion type ut = -(-Δ)mu - tα|u|(p-1)u, with p > 1, α > 0, m ≧ 2, with singular initial data u0(x) ≢ 0 such that u0(x) = 0 for any x ≠ 0, is studied. The additional multiplier h(t) = tα → 0 as t → 0 in the absorption term plays a role of a time-dependent non-homogeneous potential that affects the strength of the absorption term in the PDE. Existence and nonexistence of the corresponding very singular solutions (VSSs) is studied. For m = 1 and h(t) ≡ 1, first nonexistence result for p ≧ p0 = 1 + 2/N was proved in the celebrated paper by Brezis and Friedman in 1983. Existence of VSSs in the complement interval 1 < p < p0 was established in the middle of the 1980s. The main goal is to justify that, in the subcritical range 1 < p < p0 = 1 + {2m(1+α)}/N, there exists a finite number of different VSSs of the self-similar form u*(x,t) = t(-β)V(y), y = x/t(1/2m), β = (1+α)/(p-1), where each V is an exponentially decaying as y → ∞ solution of the elliptic equation -(-Δ)mV + 1/2my・∇V + βV - |V|(p-1)V = 0 in RN. Complicated families of VSSs in 1D and also non-radial VSS patterns in RN are detected. Some of these VSS profiles Vl are shown to bifurcate from 0 at the bifurcation exponents pl = 1 + {2m(1+α)}/(l+N), where l = 0,1,2,...","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":"35K55(MSC2010)"},{"subitem_text_value":"35K40(MSC2010)"},{"subitem_text_value":"35K65(MSC2010)"}]},"item_4_text_33":{"attribute_name":"原稿受領日","attribute_value_mlt":[{"subitem_text_value":"2007-11-05"}]},"item_4_text_4":{"attribute_name":"著者所属","attribute_value_mlt":[{"subitem_text_value":"Department of Mathematical Sciences, University of Bath"}]},"item_creator":{"attribute_name":"著者","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{"creatorName":"Galaktionov, V. A."}],"nameIdentifiers":[{"nameIdentifier":"92500","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":"jms170401.PDF","filesize":[{"value":"2.4 MB"}],"format":"application/pdf","licensetype":"license_note","mimetype":"application/pdf","url":{"label":"jms170401.PDF","url":"https://repository.dl.itc.u-tokyo.ac.jp/record/40049/files/jms170401.PDF"},"version_id":"2c32449f-fff0-4277-88e9-8e32bd8eb2eb"}]},"item_keyword":{"attribute_name":"キーワード","attribute_value_mlt":[{"subitem_subject":"The Cauchy problem","subitem_subject_scheme":"Other"},{"subitem_subject":"diffusion equations with absorption","subitem_subject_scheme":"Other"},{"subitem_subject":"initial Dirac mass","subitem_subject_scheme":"Other"},{"subitem_subject":"very singular solutions","subitem_subject_scheme":"Other"},{"subitem_subject":"existence","subitem_subject_scheme":"Other"},{"subitem_subject":"nonexistence","subitem_subject_scheme":"Other"},{"subitem_subject":"bifurcations","subitem_subject_scheme":"Other"},{"subitem_subject":"branching","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":"Vast Multiplicity of Very Singular Self-Similar Solutions of a Semilinear Higher-Order Diffusion Equation with Time-Dependent Absorption","item_titles":{"attribute_name":"タイトル","attribute_value_mlt":[{"subitem_title":"Vast Multiplicity of Very Singular Self-Similar Solutions of a Semilinear Higher-Order Diffusion Equation with Time-Dependent Absorption"}]},"item_type_id":"4","owner":"1","path":["6920","6922"],"pubdate":{"attribute_name":"公開日","attribute_value":"2012-10-22"},"publish_date":"2012-10-22","publish_status":"0","recid":"40049","relation_version_is_last":true,"title":["Vast Multiplicity of Very Singular Self-Similar Solutions of a Semilinear Higher-Order Diffusion Equation with Time-Dependent Absorption"],"weko_creator_id":"1","weko_shared_id":null},"updated":"2022-12-19T04:15:02.091231+00:00"}