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Singularity Analysis of Solutions to the Boltzmann Equation near the Boundary

Research Project

Project/Area Number 15K17572
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeMulti-year Fund
Research Field Mathematical analysis
Research InstitutionKyoto University

Principal Investigator

Chen I-Kun  京都大学, 情報学研究科, 特定講師 (10748833)

Research Collaborator HSIA Chun-Hsiung  
LIU Tai-Ping  
TAKATA Shigeru  
FUNAGANE Hitoshi  
KAWAGOE Daisuke  
Project Period (FY) 2015-04-01 – 2018-03-31
Project Status Completed (Fiscal Year 2017)
Budget Amount *help
¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2017: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2016: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2015: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Keywords偏微分方程式 / 境界値問題 / Kinetic Theory / 特異性 / Boltzman 方程式 / Boltzmann方程式 / Boltzmann 方程式
Outline of Final Research Achievements

We have shown some regularity issues of solutions to boundary value problems of the stationary Boltzmann equation, in particular singularity near the boundary and regularity inside the domain. The Boltzmann equation describes the motion of dilute gas molecule, and we consider that the results of this study will contribute to the design of nuclear reactors and aircraft.
We also considered the boundary value problem of the stationary transport equation, which is a similar equation to the stationary linearized Boltzmann equation, and succeeded in describing the discontinuity of the solution arising from discontinuous boundary data. This result is expected to be applied to the Diffused Optical Tomography, which is the next generation medical imaging technology using near infrared light.

Report

(4 results)
  • 2017 Annual Research Report   Final Research Report ( PDF )
  • 2016 Research-status Report
  • 2015 Research-status Report
  • Research Products

    (18 results)

All 2018 2017 2016 2015

All Journal Article (5 results) (of which Int'l Joint Research: 2 results,  Peer Reviewed: 4 results) Presentation (13 results) (of which Int'l Joint Research: 1 results,  Invited: 9 results)

  • [Journal Article] Regularity of stationary solutions to the linearized Boltzmann equations2018

    • Author(s)
      I-Kun Chen
    • Journal Title

      SIAM Journal on Mathematical Analysis

      Volume: 50 (1) Issue: 1 Pages: 138-161

    • DOI

      10.1137/16m1099844

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Propagation of Boundary-Induced Discontinuity in Stationary Radiative Transfer2018

    • Author(s)
      Daisuke Kawagoe, I.-Kun Chen
    • Journal Title

      Journal of Statistical Physics

      Volume: 170 (1) Issue: 1 Pages: 127-140

    • DOI

      10.1007/s10955-017-1922-8

    • NAID

      120006647342

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Regularity of stationary solutions to the linearized Boltzmann equations2016

    • Author(s)
      Chen, I-K
    • Journal Title

      arXiv:1604.03653

      Volume: -

    • Related Report
      2016 Research-status Report
  • [Journal Article] Singularity of the velocity distribution function in molecular velocity space.2016

    • Author(s)
      Chen, I-Kun; Funagane, Hitoshi; Liu, Tai-Ping; Takata, Shigeru
    • Journal Title

      Comm. Math. Phys.

      Volume: 341 no.1 Pages: 105-134

    • NAID

      120006954066

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Singularity of macroscopic variables near boundary for gases with cutoff hard potential.2015

    • Author(s)
      Chen, I-Kun; Hsia, Chun-Hsiung
    • Journal Title

      SIAM J. Math. Anal.

      Volume: 47 no.6 Pages: 4332-4349

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Presentation] Regularity of stationary linearized Boltzmann equations2017

    • Author(s)
      Chen, I-K
    • Organizer
      The 25th annual workshop on differential equations
    • Place of Presentation
      National Chiao Tung University,Hsinchu(Taiwan)
    • Year and Date
      2017-01-07
    • Related Report
      2016 Research-status Report
    • Invited
  • [Presentation] Regularity for diffuse reflection boundary problem to the stationary linearized Boltzmann equation in a convex domain2017

    • Author(s)
      I-Kun Chen
    • Organizer
      Karlstad Applied Analysis Seminar
    • Related Report
      2017 Annual Research Report
    • Invited
  • [Presentation] Regularity for diffuse reflection boundary problem to the stationary linearized Boltzmann equation in a convex domain2017

    • Author(s)
      I-Kun Chen
    • Organizer
      応用解析セミナー
    • Related Report
      2017 Annual Research Report
    • Invited
  • [Presentation] Regularity for diffuse reflection boundary problem to the stationary linearized Boltzmann equation in a convex domain2017

    • Author(s)
      I-Kun Chen
    • Organizer
      非線形解析セミナー@大岡山
    • Related Report
      2017 Annual Research Report
    • Invited
  • [Presentation] Regularity for diffuse reflection boundary problem to the stationary linearized Boltzmann equation in a convex domain2017

    • Author(s)
      I-Kun Chen
    • Organizer
      名工大非線形解析セミナー
    • Related Report
      2017 Annual Research Report
    • Invited
  • [Presentation] Singularity and regularity for the stationary linearized Boltzmann equations2016

    • Author(s)
      Chen, I-K
    • Organizer
      2016 Taiwan-Japan workshop on dispersion, Navier Stoke, kinetic, and inverse problem
    • Place of Presentation
      National Cheng Kung University,Tainan(Taiwan)
    • Year and Date
      2016-12-25
    • Related Report
      2016 Research-status Report
    • Invited
  • [Presentation] Regularity of stationary linearized Boltzmann equations2016

    • Author(s)
      Chen, I-K
    • Organizer
      The 18th RIMS workshop on mathematical analysis in fluid and gas dynamics
    • Place of Presentation
      京都大学数理解析研究所(京都府・京都市)
    • Year and Date
      2016-07-06
    • Related Report
      2016 Research-status Report
    • Invited
  • [Presentation] Regularity of stationary linearized Boltzmann equations2016

    • Author(s)
      Chen, I-K
    • Organizer
      Taiwan-Japan joint workshop on inverse problem
    • Place of Presentation
      京都大学大学院情報学研究科(京都府・京都市)
    • Year and Date
      2016-04-02
    • Related Report
      2016 Research-status Report
    • Invited
  • [Presentation] Regularity of stationary linearized Boltzmann equations2016

    • Author(s)
      Chen, I-K
    • Organizer
      NLPDE seminar
    • Place of Presentation
      京都大学数学教室(京都府・京都市)
    • Related Report
      2016 Research-status Report
  • [Presentation] Regularity of stationary linearized Boltzmann equations2016

    • Author(s)
      Chen, I-K
    • Organizer
      One-day workshop on kinetic theory
    • Place of Presentation
      Department of Math- ematics, the Chinese university of Hung Kong(People's Republic of China)
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] On boundary singularity in kinetic theory2015

    • Author(s)
      Chen, I-Kun
    • Organizer
      Seminar on Nonlinear Analysis at O-okayama
    • Place of Presentation
      東京工業大学(東京都・目黒区)
    • Year and Date
      2015-11-27
    • Related Report
      2015 Research-status Report
  • [Presentation] On boundary singularity in kinetic theory2015

    • Author(s)
      Chen, I-Kun
    • Organizer
      Mathematics for Nonlinear Phenomena: Analysis and Computation
    • Place of Presentation
      札幌コンベンションセンター(北海道・札幌市)
    • Year and Date
      2015-08-16
    • Related Report
      2015 Research-status Report
  • [Presentation] On boundary singularity in kinetic theory2015

    • Author(s)
      Chen, I-Kun
    • Organizer
      九州PDEセミナー
    • Place of Presentation
      福岡大学(福岡県・福岡市)
    • Year and Date
      2015-06-19
    • Related Report
      2015 Research-status Report

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Published: 2015-04-16   Modified: 2019-03-29  

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