On asymptotic behavior and interface curve of solution for Keller-Segel system of degenerate type

简并型Keller-Segel系统的渐近行为和解的界面曲线

• 批准号: 21540197
• 负责人: SUGIYAMA Yoshie
• 金额: $ 2.91万
• 依托单位: Osaka City University (2011)Tsuda College (2009-2010)
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2009
• 资助国家: 日本
• 起止时间: 2009 至 2011
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-21540197/
• 关键词: 退化型; Keller-Segel系; 爆発解; 測度値解; 有限時間爆発; 時間大域解; 退化放物型方程式; デルタ関数; 退化型Keller-Segel系; 界面曲線; 有限伝播性; 部分正則性定理

Measure valued solution : The time global solution has been constructed for Keller-Segel system of semi-linear type by expanding the functional space to the measure valued solution.Asymptotics : We have proved that the solution of Keller-Segel system behaves like a stationary solution asymptotically as time tends to infinity.Uniqueness : We have established the functional space which the weak solution becomes unique.Finite speed propagation : The existence of solution and the extinction phenomena has been proved for Keller-Segel system of singular type.

测度值解：通过将泛函空间扩展到测度值解，构造了半线性型Keller-Segel系统的时间全局解。渐近性：我们证明了Keller-Segel系统的解在时间趋于无穷时渐近表现为平稳解。唯一性：我们建立了弱解唯一的功能空间。有限速度传播：证明了奇异型Keller-Segel系统解的存在性和消光现象。

项目成果

Strong solutions to the Keller‐Segel system with the weak Ln /2 initial data and its application to the blow‐up rate

• DOI: 10.1002/mana.200610835
• 发表时间: 2010-05
• 期刊: Mathematische Nachrichten
• 影响因子: 1
• 作者: H. Kozono;Y. Sugiyama

On ε-Regularity Theorem and Asymptotic Behaviors of Solutions for Keller-Segel Systems

• DOI: 10.1137/080721078
• 发表时间: 2009-10
• 期刊: SIAM J. Math. Anal.
• 作者: Y. Sugiyama

Self-similar blow-up with a continuo-us range of values of the aggregated mass for a degenerate Keller-Segel system

简并 Keller-Segel 系统具有连续聚合质量值范围的自相似爆炸

• 发表时间: 2011
• 期刊: Advances in Differential Equations
• 影响因子: 1.4
• 作者: Bony;Fujiie;Ramond;Zerzeri;Y. Sugiyama and J. J. L. Velazquez
• 通讯作者: Y. Sugiyama and J. J. L. Velazquez

Finite speed of propagation in 1-D degenerate Keller-Segel system

一维简并 Keller-Segel 系统中的有限传播速度

• DOI: 10.1002/mana.200810258
• 发表时间: 2012
• 期刊: Mathematische Nachrichten
• 影响因子: 1
• 作者: Kozono,H.;Sugiyama,Y.;Yahagi,Y.,;Yoshie Sugiyama
• 通讯作者: Yoshie Sugiyama

Self-similar blow-up with a continuous range of values of the aggregated mass for a degenerate Keller-Segel system

简并 Keller-Segel 系统的具有连续聚合质量值范围的自相似爆炸

• 发表时间: 2011
• 期刊: Advances in Differential Equations
• 影响因子: 1.4
• 作者: Y.Sugiyama;J.J.L.Velazquez
• 通讯作者: J.J.L.Velazquez