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数理生物学に現れる非線形発展方程式の数学解析

Research Project

Project/Area Number 21K03278
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Review Section Basic Section 12010:Basic analysis-related
Research InstitutionTokyo University of Science

Principal Investigator

横田 智巳  東京理科大学, 理学部第一部数学科, 教授 (60349826)

Project Period (FY) 2021-04-01 – 2025-03-31
Project Status Granted (Fiscal Year 2023)
Budget Amount *help
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2024: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2023: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2022: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2021: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Keywords走化性方程式 / 解の漸近挙動 / 非線形拡散 / 作用素論 / 非線形発展方程式
Outline of Research at the Start

本研究は, 走化性方程式という生物の集中現象を記述する数理モデルを研究対象とする. 特に方程式の解が時間大域的に存在するかどうかという問に対して, 方程式に現れる関数や定数に対してどのような条件を課せばよいかということを明らかにする. このような問題は, 様々な設定の下で様々な研究が分散して行われているのが現状であり, それ打破するような研究を実施する. その中には, まだ解明されていない問題の解決も含まれる. また, 関連する研究として, 反応の時差を考慮に入れた微分方程式に対する汎用性の高い適切性理論を構築し、先述の走化性方程式の研究との相乗効果を図る.

Outline of Annual Research Achievements

本研究は, 生物の集中現象を記述する様々なタイプの走化性方程式を研究対象としている. 具体的な課題としては,解が時間大域的に存在して時間について一様に有界となるか,あるいは解が有限時刻で爆発するかという問題に対して, 方程式に現れる関数や定数に対してどのような条件を課せばよいかということを明らかにしていく. 2023年度は,次の2つの研究を中心に実施した.

研究1.ロジスティック項をもつ摩擦制限型走化性方程式系の解の爆発に関する研究
研究2.単純化した癌浸潤モデルの解の有限時刻爆発に関する研究

研究1については,2022年度に続いてイタリア・カリアリ大学のMonica Marras氏、Stella Vernier-Piro氏との共同研究を実施し,2023年度はロジスティック項をもつ場合に, 有限時刻で爆発する解の存在と爆発時刻の下からの評価を「簡潔な方法」で導くことができた. 研究2については,千葉大学の石田祥子氏との共同研究を実施し, 単純化した癌浸潤モデルに対して,Lyapunov関数の構成について吟味した。研究2については、論文の形にするには至らなかったが,新しい展開が見えてきた。研究1については,得られた成果を論文にまとめ,現在専門誌に投稿中である.また,日本数学会秋季総合分科会及び年会, 発展方程式研究会等の国内学会, 国際会議「The 13th AIMS Conference on Dynamical Systems, Differential Equations and Applications」(2023年5-6月,アメリカ),「Nonlinear Phenomena in Biology, Ecology, Phisics and Mechanics」(2023年10月, アゼルバイジャン)などで本研究課題に関わる研究成果を報告した.

Current Status of Research Progress
Current Status of Research Progress

2: Research has progressed on the whole more than it was originally planned.

Reason

摩擦制限型走化性方程式系の解の爆発に関する研究については, 2023年度までにロジスティック項をもつ場合まで解決することができ, 今後の研究指針を決めるための重要な研究成果が得られた. そのような意味では, 当初の計画以上に進展しているが, もう1つの研究課題である, 遅延を含む走化性方程式系に関する研究については, 研究課題の設定の見直ししており, 難航している. 代わりに, 退化型拡散を伴う癌浸潤モデルや他の関連する走化性方程式の解の漸近挙動に関する研究が進んだ. これらを総合して, おおむね順調に進展していると判断した.

Strategy for Future Research Activity

2024年度の研究に向けて,退化型拡散を伴う癌浸潤モデルについては, まず解の有限時刻爆発が起こるかどうかを明確にすることが推進方策であると考えている. また, 遅延を含む走化性方程式については, 非局所項をもつモデルの研究を参考にして時間大域解の存在から示すことを考えている.摩擦制限型の走化性方程式の研究については,イタリア・カリアリ大学のMonica Marras氏らと共同で研究の完成を図る.研究代表者の大学院生の小波津晶平氏や水上雅昭氏,千代祐太朗氏,田中悠也氏に協力してもらうことで研究の推進が期待できる.

Report

(3 results)
  • 2023 Research-status Report
  • 2022 Research-status Report
  • 2021 Research-status Report
  • Research Products

    (46 results)

All 2024 2023 2022 2021 Other

All Int'l Joint Research (5 results) Journal Article (22 results) (of which Int'l Joint Research: 5 results,  Peer Reviewed: 22 results,  Open Access: 3 results) Presentation (19 results) (of which Int'l Joint Research: 5 results,  Invited: 8 results)

  • [Int'l Joint Research] パーダーボルン大学(ドイツ)

    • Related Report
      2023 Research-status Report
  • [Int'l Joint Research] カリアリ大学(イタリア)

    • Related Report
      2023 Research-status Report
  • [Int'l Joint Research] パーダーボルン大学(ドイツ)

    • Related Report
      2022 Research-status Report
  • [Int'l Joint Research] カリアリ大学(イタリア)

    • Related Report
      2022 Research-status Report
  • [Int'l Joint Research] Universit`a di Cagliari(イタリア)

    • Related Report
      2021 Research-status Report
  • [Journal Article] Boundedness criteria for a class of indirect (and direct) chemotaxis-consumption models with signal-dependent sensitivity in high dimensions2024

    • Author(s)
      Chiyo Yutaro、Sugawara Kazuma、Yokota Tomomi
    • Journal Title

      Applied Mathematics Letters

      Volume: 149 Pages: 108908-108908

    • DOI

      10.1016/j.aml.2023.108908

    • Related Report
      2023 Research-status Report
    • Peer Reviewed
  • [Journal Article] Stability of constant equilibria in a Keller-Segel system with gradient dependent chemotactic sensitivity2023

    • Author(s)
      S. Kohatsu, T. Yokota
    • Journal Title

      LE MATEMATICHE

      Volume: 78 Pages: 213-237

    • Related Report
      2023 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Behavior in time of solutions of a Keller?Segel system with flux limitation and source term2023

    • Author(s)
      Marras Monica、Vernier-Piro Stella、Yokota Tomomi
    • Journal Title

      Nonlinear Differential Equations and Applications NoDEA

      Volume: 30 Issue: 5 Pages: 1-27

    • DOI

      10.1007/s00030-023-00874-8

    • Related Report
      2023 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Boundedness and weak stabilization in a degenerate chemotaxis model arising from tumor invasion2023

    • Author(s)
      Ishida Sachiko、Yokota Tomomi
    • Journal Title

      Journal of Differential Equations

      Volume: 371 Pages: 450-480

    • DOI

      10.1016/j.jde.2023.06.028

    • Related Report
      2023 Research-status Report
    • Peer Reviewed
  • [Journal Article] Avoiding critical mass phenomena by arbitrarily mild saturation of cross-diffusive fluxes in two-dimensional Keller-Segel-Navier-Stokes systems2023

    • Author(s)
      Winkler Michael、Yokota Tomomi
    • Journal Title

      Journal of Differential Equations

      Volume: 374 Pages: 1-28

    • DOI

      10.1016/j.jde.2023.07.029

    • Related Report
      2023 Research-status Report
    • Peer Reviewed
  • [Journal Article] Stabilization in degenerate parabolic equations in divergence form and application to chemotaxis systems2023

    • Author(s)
      Sachiko Ishida, Tomomi Yokota
    • Journal Title

      Archivum Mathematicum

      Volume: 59 Issue: 2 Pages: 181-189

    • DOI

      10.5817/am2023-2-181

    • Related Report
      2022 Research-status Report
    • Peer Reviewed
  • [Journal Article] Global asymptotic stability of endemic equilibria for a diffusive SIR epidemic model with saturated incidence and logistic growth2023

    • Author(s)
      Yutaro Chiyo, Yuya Tanaka, Ayako Uchida, Tomomi Yokota
    • Journal Title

      Discrete and Continuous Dynamical Systems. Series B

      Volume: 28 Issue: 3 Pages: 2184-2210

    • DOI

      10.3934/dcdsb.2022163

    • Related Report
      2022 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Finite-time blow-up in a quasilinear degenerate parabolic-elliptic chemotaxis system with logistic source and nonlinear production2023

    • Author(s)
      Yuya Tanaka, Tomomi Yokota
    • Journal Title

      Discrete and Continuous Dynamical Systems. Series B

      Volume: 28 Issue: 1 Pages: 262-286

    • DOI

      10.3934/dcdsb.2022075

    • Related Report
      2022 Research-status Report
    • Peer Reviewed
  • [Journal Article] Global existence and stabilization in a diffusive predator-prey model with population flux by attractive transition2023

    • Author(s)
      Frederic Heihoff, Tomomi Yokota
    • Journal Title

      Nonlinear Analysis. Real World Applications

      Volume: 69 Pages: 1-24

    • DOI

      10.1016/j.nonrwa.2022.103757

    • Related Report
      2022 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Application of weak stabilization theory for degenerate parabolic equations in divergence form to a chemotaxis model for tumor invasion2022

    • Author(s)
      Ishida Sachiko、Yokota Tomomi
    • Journal Title

      Discrete and Continuous Dynamical Systems - B

      Volume: 28 Issue: 10 Pages: 5296-5306

    • DOI

      10.3934/dcdsb.2022256

    • Related Report
      2023 Research-status Report
    • Peer Reviewed
  • [Journal Article] Boundedness and finite-time blow-up in a quasilinear parabolic-elliptic-elliptic attraction-repulsion chemotaxis system2022

    • Author(s)
      Yutaro Chiyo, Tomomi Yokota
    • Journal Title

      Zeitschrift fur Angewandte Mathematik und Physik

      Volume: 73 Issue: 2 Pages: 1-27

    • DOI

      10.1007/s00033-022-01695-y

    • Related Report
      2022 Research-status Report
    • Peer Reviewed
  • [Journal Article] Weak stabilization in degenerate parabolic equations in divergence form: application to degenerate Keller--Segel systems2022

    • Author(s)
      Ishida Sachiko、Yokota Tomomi
    • Journal Title

      Calculus of Variations and Partial Differential Equations

      Volume: 61 Issue: 3 Pages: 1-21

    • DOI

      10.1007/s00526-022-02203-w

    • Related Report
      2022 Research-status Report
    • Peer Reviewed
  • [Journal Article] Stabilization for small mass in a quasilinear parabolic-elliptic-elliptic attraction-repulsion chemotaxis system with density-dependent sensitivity: balanced case2022

    • Author(s)
      Yutaro Chiyo, Tomomi Yokota
    • Journal Title

      Le Matematiche

      Volume: 77 Pages: 203-223

    • Related Report
      2022 Research-status Report
    • Peer Reviewed
  • [Journal Article] Blow-up phenomena for a chemotaxis system with flux limitation2022

    • Author(s)
      Monica Marras, Stella Verner-Piro, Tomomi Yokota
    • Journal Title

      Journal of Mathematical Analysis and Applications

      Volume: 515 Issue: 1 Pages: 1-13

    • DOI

      10.1016/j.jmaa.2022.126376

    • Related Report
      2022 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Can chemotactic effects lead to blow-up or not in two-species chemotaxis-competition models?2022

    • Author(s)
      Masaaki Mizukami, Yuya Tanaka, Tomomi Yokota
    • Journal Title

      Zeitschrift fur Angewandte Mathematik und Physik

      Volume: 73 Issue: 6 Pages: 1-25

    • DOI

      10.1007/s00033-022-01878-7

    • Related Report
      2022 Research-status Report
    • Peer Reviewed
  • [Journal Article] Boundedness in a fully parabolic attraction-repulsion chemotaxis system with nonlinear diffusion and signal-dependent sensitivity2022

    • Author(s)
      Yutaro Chiyo, Tomomi Yokota
    • Journal Title

      Nonlinear Analysis. Real World Applications

      Volume: 66 Pages: 1-23

    • DOI

      10.1016/j.nonrwa.2022.103533

    • Related Report
      2022 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Global existence and boundedness in a supercritical quasilinear degenerate Keller-Segel system under relaxed smallness conditions for initial data2022

    • Author(s)
      Tsukasa Ogawa, Tomomi Yokota
    • Journal Title

      Acta Applicandae Mathematicae

      Volume: 180 Issue: 1 Pages: 1-22

    • DOI

      10.1007/s10440-022-00504-y

    • Related Report
      2022 Research-status Report
    • Peer Reviewed
  • [Journal Article] Equilibration in a two-species-two-chemicals chemotaxis-competition system2021

    • Author(s)
      Masaaki Mizukami, Tomomi Yokota, Natsumi Yoshimiya
    • Journal Title

      LE MATEMATICHE

      Volume: 76 Pages: 171-191

    • Related Report
      2021 Research-status Report
    • Peer Reviewed
  • [Journal Article] Existence of bounded global solutions for fully parabolic attraction-repulsion chemotaxis systems with signal-dependent sensitivities and without logistic source2021

    • Author(s)
      Yutaro Chiyo, Masaaki Mizukami, Tomomi Yokota
    • Journal Title

      Electronic Journal of Differential Equations

      Volume: 71 Pages: 1-10

    • Related Report
      2021 Research-status Report
    • Peer Reviewed
  • [Journal Article] Remarks on two connected papers about Keller-Segel systems with nonlinear production2021

    • Author(s)
      Tanaka Yuya、Viglialoro Giuseppe、Yokota Tomomi
    • Journal Title

      Journal of Mathematical Analysis and Applications

      Volume: 501 Issue: 2 Pages: 1-5

    • DOI

      10.1016/j.jmaa.2021.125188

    • Related Report
      2021 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Blow-up phenomena in a parabolic-elliptic-elliptic attraction-repulsion chemotaxis system with superlinear logistic degradation2021

    • Author(s)
      Chiyo Yutaro、Marras Monica、Tanaka Yuya、Yokota Tomomi
    • Journal Title

      Nonlinear Analysis

      Volume: 212 Pages: 112550-112550

    • DOI

      10.1016/j.na.2021.112550

    • Related Report
      2021 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Solvability in abstract evolution equations with countable time delays in Banach spaces: Global Lipschitz perturbation2021

    • Author(s)
      Yokota Tomomi、Yoshii Kentarou
    • Journal Title

      Evolution Equations & Control Theory

      Volume: 10 Issue: 4 Pages: 689-689

    • DOI

      10.3934/eect.2020086

    • Related Report
      2021 Research-status Report
    • Peer Reviewed
  • [Presentation] Boundedness and blow-up in a quasilinear chemotaxis system with logistic source2024

    • Author(s)
      Tomomi Yokota
    • Organizer
      Partial Differential. Equations Seminar
    • Related Report
      2023 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Global Dynamics in a Degenerate Chemotaxis Model for Tumor Invasion2023

    • Author(s)
      Tomomi Yokota
    • Organizer
      The 13th AIMS Conference on Dynamical Systems, Differential Equations and Applications
    • Related Report
      2023 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Boundedness and blow-up of solutions to a quasilinear chemotaxis system2023

    • Author(s)
      Tomomi Yokota
    • Organizer
      Seminary on Parabolic Problems and applications
    • Related Report
      2023 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Boundedness in a Degenerate Chemotaxis System for Tumor Invasion2023

    • Author(s)
      Tomomi Yokota
    • Organizer
      Nonlinear Phenomena in Biology, Ecology, Physics and Mechanics
    • Related Report
      2023 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Finite-time blow-up of weak solutions to a degenerate chemotaxis system with logistic source2023

    • Author(s)
      横田智巳
    • Organizer
      RIMS 共同研究(公開型) 関数空間論とその周辺
    • Related Report
      2022 Research-status Report
    • Invited
  • [Presentation] Behavior of weak solutions to a Keller-Segel system with gradient dependent chemotactic coefficient2023

    • Author(s)
      小波津晶平、横田智巳
    • Organizer
      日本数学会年会 実函数論分科会
    • Related Report
      2022 Research-status Report
  • [Presentation] Stabilization in degenerate parabolic equations in divergence form and application to chemotaxis systems2022

    • Author(s)
      横田智巳
    • Organizer
      EQUADIFF 15 Conference on Differential Equations and Their Applications
    • Related Report
      2022 Research-status Report
    • Int'l Joint Research
  • [Presentation] Analysis of degenerate chemotaxis systems with/without logistic source2022

    • Author(s)
      横田智巳
    • Organizer
      第61回実函数論・函数解析学合同シンポジウム
    • Related Report
      2022 Research-status Report
    • Invited
  • [Presentation] Blow-up of maximal weak solutions to a degenerate chemotaxis system with logistic source2022

    • Author(s)
      横田智巳
    • Organizer
      黒木場正城教授 追悼研究集会「非線型偏微分方程式と走化性」
    • Related Report
      2022 Research-status Report
    • Invited
  • [Presentation] Does blow-up occur in two-species chemotaxis-competition models?2022

    • Author(s)
      田中悠也, 水上雅昭,横田智巳
    • Organizer
      第48回発展方程式研究会
    • Related Report
      2022 Research-status Report
  • [Presentation] Occurrence of blow-up phenomena by chemotactic effects in a two species chemotaxis-competition model2022

    • Author(s)
      水上雅昭、田中悠也、横田智巳
    • Organizer
      日本数学会秋季総合分科会 函数方程式論分科会
    • Related Report
      2022 Research-status Report
  • [Presentation] Stabilization in a quasilinear attraction-repulsion chemotaxis system: balanced case2022

    • Author(s)
      千代祐太朗、横田智巳
    • Organizer
      日本数学会秋季総合分科会 実函数論分科会
    • Related Report
      2022 Research-status Report
  • [Presentation] Boundedness in an attraction-repulsion chemotaxis system with nonlinear diffusion and singular sensitivity2021

    • Author(s)
      千代祐太朗、水上雅昭、横田智巳
    • Organizer
      日本数学会秋季総合分科会 実函数論分科会
    • Related Report
      2021 Research-status Report
  • [Presentation] Stabilization in degenerate parabolic equations in divergence form and application to Keller-Segel systems2021

    • Author(s)
      横田智巳
    • Organizer
      RIMS研究集会(公開型)「発展方程式の広がり:理論的基礎から実践的応用まで」
    • Related Report
      2021 Research-status Report
    • Invited
  • [Presentation] Asymptotic stabilization in a simplified quasilinear attraction-repulsion chemotaxis system2021

    • Author(s)
      千代祐太朗, 横田智巳
    • Organizer
      第47回発展方程式研究会
    • Related Report
      2021 Research-status Report
  • [Presentation] Blow-up in nondegenerate and degenerate chemotaxis systems with logistic source and nonlinear production2021

    • Author(s)
      田中悠也, 横田智巳
    • Organizer
      第47回発展方程式研究会
    • Related Report
      2021 Research-status Report
  • [Presentation] Large time behavior for weak solutions of parabolic equations with L^1-conservation law2021

    • Author(s)
      石田祥子, 横田智巳
    • Organizer
      第47回発展方程式研究会
    • Related Report
      2021 Research-status Report
  • [Presentation] Blow-up in a degenerate parabolic-elliptic chemotaxis system with logistic source and nonlinear production2021

    • Author(s)
      田中悠也, 横田智巳
    • Organizer
      日本数学会年会 函数方程式論分科会
    • Related Report
      2021 Research-status Report
  • [Presentation] 日本数学会年会 実函数論分科会2021

    • Author(s)
      千代祐太朗, 横田智巳
    • Organizer
      日本数学会年会 実函数論分科会
    • Related Report
      2021 Research-status Report

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Published: 2021-04-28   Modified: 2024-12-25  

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