WEKO3
アイテム
{"_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": ["6920", "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 \u003e 1, α \u003e 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 \u003c p \u003c p0 was established in the middle of the 1980s. The main goal is to justify that, in the subcritical range 1 \u003c p \u003c 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_34": {"attribute_name": "資源タイプ", "attribute_value_mlt": [{"subitem_text_value": "Departmental Bulletin Paper"}]}, "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", "download_preview_message": "", "file_order": 0, "filename": "jms170401.PDF", "filesize": [{"value": "2.4 MB"}], "format": "application/pdf", "future_date_message": "", "is_thumbnail": false, "licensetype": "license_free", "mimetype": "application/pdf", "size": 2400000.0, "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"], "permalink_uri": "http://hdl.handle.net/2261/52406", "pubdate": {"attribute_name": "公開日", "attribute_value": "2012-10-22"}, "publish_date": "2012-10-22", "publish_status": "0", "recid": "40049", "relation": {}, "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_shared_id": null}
Vast Multiplicity of Very Singular Self-Similar Solutions of a Semilinear Higher-Order Diffusion Equation with Time-Dependent Absorption
http://hdl.handle.net/2261/52406
http://hdl.handle.net/2261/52406687d06bf-41b1-4888-afb6-119a7cd80be1
名前 / ファイル | ライセンス | アクション |
---|---|---|
jms170401.PDF (2.4 MB)
|
|
Item type | 紀要論文 / Departmental Bulletin Paper(1) | |||||
---|---|---|---|---|---|---|
公開日 | 2012-10-22 | |||||
タイトル | ||||||
タイトル | Vast Multiplicity of Very Singular Self-Similar Solutions of a Semilinear Higher-Order Diffusion Equation with Time-Dependent Absorption | |||||
言語 | ||||||
言語 | eng | |||||
キーワード | ||||||
主題 | The Cauchy problem | |||||
主題Scheme | Other | |||||
キーワード | ||||||
主題 | diffusion equations with absorption | |||||
主題Scheme | Other | |||||
キーワード | ||||||
主題 | initial Dirac mass | |||||
主題Scheme | Other | |||||
キーワード | ||||||
主題 | very singular solutions | |||||
主題Scheme | Other | |||||
キーワード | ||||||
主題 | existence | |||||
主題Scheme | Other | |||||
キーワード | ||||||
主題 | nonexistence | |||||
主題Scheme | Other | |||||
キーワード | ||||||
主題 | bifurcations | |||||
主題Scheme | Other | |||||
キーワード | ||||||
主題 | branching | |||||
主題Scheme | Other | |||||
資源タイプ | ||||||
資源 | http://purl.org/coar/resource_type/c_6501 | |||||
タイプ | departmental bulletin paper | |||||
著者 |
Galaktionov, V. A.
× Galaktionov, V. A. |
|||||
著者所属 | ||||||
著者所属 | Department of Mathematical Sciences, University of Bath | |||||
抄録 | ||||||
内容記述タイプ | Abstract | |||||
内容記述 | 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,... | |||||
書誌情報 |
Journal of mathematical sciences, the University of Tokyo 巻 17, 号 4, p. 323-358, 発行日 2011-03-29 |
|||||
ISSN | ||||||
収録物識別子タイプ | ISSN | |||||
収録物識別子 | 13405705 | |||||
書誌レコードID | ||||||
収録物識別子タイプ | NCID | |||||
収録物識別子 | AA11021653 | |||||
日本十進分類法 | ||||||
主題 | 415 | |||||
主題Scheme | NDC | |||||
Mathematical Reviews Number | ||||||
MR | ||||||
Mathmatical Subject Classification | ||||||
35K55(MSC2010) | ||||||
Mathmatical Subject Classification | ||||||
35K40(MSC2010) | ||||||
Mathmatical Subject Classification | ||||||
35K65(MSC2010) | ||||||
出版者 | ||||||
出版者 | Graduate School of Mathematical Sciences, The University of Tokyo | |||||
原稿受領日 | ||||||
2007-11-05 |