Singular Limit Problem to the Keller-Segel System in Critical Spaces and Related Medical Problems—An Application of Maximal Regularity

Takayoshi Ogawa

研究成果: Conference contribution

抄録

We consider singular limit problems of the Cauchy problem for the Patlak-Keller-Segel equation and related problems appeared in the theory of medical and biochemical dynamics. It is shown that the solution to the Patlak-Keller-Segel equation in a scaling critical function class converges strongly to a solution of the drift-diffusion system of parabolic-elliptic equations as the relaxation time parameter τ→ ∞. Analogous problem related to the Chaplain-Anderson model for cancer growth model is also presented as well as Arzhimer’s model that involves the multi-component drift-diffusion system. For the proof, we use generalized maximal regularity for the heat equations and systematically apply embeddings between the interpolation spaces shown in [40, 41]. The argument requires generalized version of maximal regularity developed in [40, 61], for the Cauchy problem of the heat equation.

本文言語English
ホスト出版物のタイトルNonlinear Partial Differential Equations for Future Applications
編集者Shigeaki Koike, Hideo Kozono, Takayoshi Ogawa, Shigeru Sakaguchi
出版社Springer
ページ103-182
ページ数80
ISBN(印刷版)9789813348219
DOI
出版ステータスPublished - 2021
イベントWorkshops on Nonlinear Partial Differential Equations for Future Applications, 2017 - Sendai, Japan
継続期間: 2017 10 22017 10 6

出版物シリーズ

名前Springer Proceedings in Mathematics and Statistics
346
ISSN(印刷版)2194-1009
ISSN(電子版)2194-1017

Conference

ConferenceWorkshops on Nonlinear Partial Differential Equations for Future Applications, 2017
国/地域Japan
CitySendai
Period17/10/217/10/6

ASJC Scopus subject areas

  • 数学 (全般)

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