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Regularity and Asymptotic Behavior for the Keller-Segel System of Degenerate Type with Critical Nonlinearity
http://hdl.handle.net/2261/59060
http://hdl.handle.net/2261/590601314203d-825f-460d-ba99-96c78d72f5e6
名前 / ファイル | ライセンス | アクション |
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jms200304.pdf (349.9 kB)
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Item type | 紀要論文 / Departmental Bulletin Paper(1) | |||||
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公開日 | 2015-12-15 | |||||
タイトル | ||||||
タイトル | Regularity and Asymptotic Behavior for the Keller-Segel System of Degenerate Type with Critical Nonlinearity | |||||
言語 | ||||||
言語 | eng | |||||
キーワード | ||||||
主題Scheme | Other | |||||
主題 | Degenerate Keller-Segel system | |||||
キーワード | ||||||
主題Scheme | Other | |||||
主題 | Hölder regularity | |||||
キーワード | ||||||
主題Scheme | Other | |||||
主題 | uniform asymptotic estimates | |||||
資源タイプ | ||||||
資源タイプ識別子 | http://purl.org/coar/resource_type/c_6501 | |||||
資源タイプ | departmental bulletin paper | |||||
著者 |
Mizuno, Masashi
× Mizuno, Masashi× Ogawa, Takayoshi |
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著者所属 | ||||||
値 | Department of Mathematics, College of Science and Technology, Nihon University | |||||
著者所属 | ||||||
値 | Mathematical Institute, Tohoku University | |||||
抄録 | ||||||
内容記述タイプ | Abstract | |||||
内容記述 | 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]. | |||||
書誌情報 |
Journal of mathematical sciences, the University of Tokyo 巻 20, 号 3, p. 375-433, 発行日 2014-01-15 |
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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Scheme | NDC | |||||
主題 | 415 | |||||
Mathematical Reviews Number | ||||||
値 | MR | |||||
Mathmatical Subject Classification | ||||||
値 | 35B40(MSC2010) | |||||
Mathmatical Subject Classification | ||||||
値 | 35B65(MSC2010) | |||||
Mathmatical Subject Classification | ||||||
値 | 35K65(MSC2010) | |||||
出版者 | ||||||
出版者 | Graduate School of Mathematical Sciences, The University of Tokyo | |||||
原稿受領日 | ||||||
値 | 2013-06-11 |