Homepage of Tatsuya Hosono

研究内容

数学の中でも非線形偏微分方程式論と呼ばれる解析学の分野を研究対象とし, 数学的構造の理解と新たな理論を構築することを目的としています. 中でも, 放物型偏微分方程式に分類される解の性質や問題に取り組んでいます.

これまで, 走化性と呼ばれる生物現象に基づいて記述される非線形放物型方程式の解の定量的, 定性的性質, 特に時間大域挙動の解析に着目してきました. 走化性とは, 細胞や生命体が, ある特定の化学物質に応答して特定の方向に沿って移動(遊走)する現象のことを指し, これは胚発生や癌の浸潤, 免疫などのメカニズムに重要な役割を果たしていると考えられています. 例えばバクテリアなどは, 周囲にある化学物質を感知して, 好ましい場合は集中したり, 好ましくない場合は離れたりします. また, 身体の免疫を担う細胞 (白血球など) は, 害を及ぼす微生物(とそれが分泌する化学物質)を感知し, その部位に遊走して貪食します.

走化性に基づいて定式化される数理モデルは連立系の放物型方程式で与えられます. 特に, 拡散と集中といった相反する構造が備わり, それらの解析的な効果の釣り合いから解の長時間安定や特異性の生成(有限時間爆発など)といった相反する挙動が起こることが知られています. 最近は, それら解の時間大域挙動に寄与する初期データの条件や, 安定と不安定が拮抗する臨界状況下での解の性質に着目し, 方程式系に内在する自由エネルギーを用いた解析や勾配流の観点から系の構造を調べることに注目しています.

論文

査読論文

1. Nonlinear Fisher information, corresponding functional inequalities and applications

Tomasz Cieślak, Kentaro Fujie and Tatsuya Hosono

Journal of Differential Equations 470 (2026), 114350.

publisher link: https://doi.org/10.1016/j.jde.2026.114350

arXiv link: https://doi.org/10.48550/arXiv.2509.01475

1. Global existence and boundedness of solutions to a fully parabolic chemotaxis system with indirect signal production in $\mathbb{R}^4$

Tatsuya Hosono and Philippe Laurençot

Journal of Differential Equations 416 (2025), 2085-2133.

publisher link: https://doi.org/10.1016/j.jde.2024.10.035

arXiv link: https://doi.org/10.48550/arXiv.2404.01724

1. Global existence of solutions to the 4D attraction-repulsion chemotaxis system and applications of Brezis--Merle inequality

Tatsuya Hosono and Takayoshi Ogawa

Nonlinearity 36 (2023), 5860-5883.

publisher link: https://doi.org/10.1088/1361-6544/acf6ee

1. Finite-time blow-up for the attractive dominant case of an attraction-repulsion chemotaxis system in the whole space

Tatsuya Hosono

Differential and Integral Equations 36 (2023), 907-928.

publisher link: https://doi.org/10.57262/die036-1112-907

1. Local well-posedness and finite time blow-up of solutions to an attraction-repulsion chemotaxis system in higher dimensions

Tatsuya Hosono and Takayoshi Ogawa

Journal of Mathematical Analysis and Applications 510 (2022), 126009.

publisher link: https://doi.org/10.1016/j.jmaa.2022.126009

Proceedings (Peer-reviewed)

1. On the Cauchy problem of a chemotaxis system with indirect signal production

Tatsuya Hosono

accepted in SEMA-SIMAI SPRINGER SERIES volume entitled “Analysis, approximation and control of chemotaxis models.”

publisher link: https://link.springer.com/chapter/10.1007/978-3-032-14789-9_4

(These proceedings are based on the mini-symposia held at the 9th European Congress of Mathematics, organized by the European Mathematical Society, which took place in Seville, Spain, from July 15 to 19, 2024.)

査読前論文

1. Global existence for the fully parabolic Keller--Segel system with critical mass on the plane

Tatsuya Hosono

arXiv link: https://arxiv.org/abs/2602.03768

1. Global solvability and threshold for a parabolic-elliptic chemotaxis system in $\mathbb R^n$

Tatsuya Hosono

OCAMI Preprint Series 2025 link: https://www.omu.ac.jp/orp/ocami/publications/preprint-series/2025/

ResearchGate

共同研究者

Takayoshi Ogawa; Philippe Laurençot; Tomasz Cieślak; Kentaro Fujie

講演・口頭発表

国際会議

EYAWKAKSAD (Everything You Always Wanted to Know About Keller-Segel and Aggregation-Diffusion), Université Lyon 1, France, April 24, 2026, invited:

Global existence for the two-dimensional fully parabolic Keller--Segel system at critical mass

Analysis Seminar at The University of Edinburgh, UK, January 19, 2026, Invited:

Nonlinear entropy production and its application to global existence for the 1D critical quasilinear Keller--Segel system

PDE seminar, EYAWKAJKOS, Université Claude Bernard - Lyon 1, December 10, 2025, Invited:

Nonlinear Fisher information and its application to 1D critical quasilinear fully parabolic Keller--Segel system

ReaDiNet2025 : A ReaDiNet workshop on deterministic and stochastic PDEs, Obernai, France, November 24-27, 2025, Invited:

Nonlinear Fisher information and its application to 1D critical quasilinear fully parabolic Keller--Segel system

PDE seminar at the Warsaw University of Technology, Warsaw University of Technology, Poland, November 6, 2025, Invited:

Nonlinear Fisher information and its application to 1D critical quasilinear fully parabolic Keller--Segel system

PDE seminar, Laboratoire de Mathématiques (LAMA), Université Savoie Mont Blanc, France, October 10, 2025, Invited:

Nonlinear Fisher information and its application to critical quasilinear fully parabolic Keller-Segel system

PDE seminar, L'Institut Elie Cartan de Lorraine, Nancy, France, September 11, 2025, Invited:

Global solvability and threshold for a parabolic-elliptic system of chemotaxis

9th European Congress of Mathematics, minisymposium, Sevilla, Spain, July 18, 2024, Invited: