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Characterization of shock profiles in terms of stabilization mechanisms in systems with weak dissipations

Research Project

Project/Area Number 26800076
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeMulti-year Fund
Research Field Mathematical analysis
Research InstitutionTokyo University of Marine Science and Technology (2015-2016)
Waseda University (2014)

Principal Investigator

Ohnawa Masashi  東京海洋大学, 学術研究院, 准教授 (10443243)

Project Period (FY) 2014-04-01 – 2017-03-31
Project Status Completed (Fiscal Year 2016)
Budget Amount *help
¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2015: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Keywords不連続衝撃波 / 漸近安定性 / 爆発 / 不連続点の合体 / 衝撃波 / 安定性 / パターン / 進行波 / 分岐 / 対流 / 弱い拡散
Outline of Final Research Achievements

In the last two decades, many systems with weaker dissipation than diffusion are found to admit discontinuous traveling wave solutions if certain parameters exceed threshold values. Examples include radiating gas systems, saturating dissipation in the Burgers type equations, and hyperbolic systems with relaxation. This study aims to explain variations in the shock profiles in terms of stabilization mechanisms. We have proved the following facts for a simplified radiating gas system called Hamer's model. i) In all subcritical cases, radiation dominates over convection and the solution converges to a traveling wave solution without blowing up. ii) There are arbitrary small perturbations around the critical shock wave which cause blow up of the solution in a finite time. iii) In the supercritical cases, the existence of a discontinuity which satisfies the entropy condition helps convection to recover stability even in the L-infinity topology.

Report

(4 results)
  • 2016 Annual Research Report   Final Research Report ( PDF )
  • 2015 Research-status Report
  • 2014 Research-status Report
  • Research Products

    (25 results)

All 2017 2016 2015 2014 Other

All Int'l Joint Research (2 results) Journal Article (7 results) (of which Peer Reviewed: 7 results,  Acknowledgement Compliant: 2 results) Presentation (12 results) (of which Int'l Joint Research: 3 results,  Invited: 7 results) Book (2 results) Remarks (2 results)

  • [Int'l Joint Research] Ulsan National Inst. of Sci. and Tech.(韓国)

    • Related Report
      2016 Annual Research Report
  • [Int'l Joint Research] Ulsan National Institute of Sci. & Tech.(韓国)

    • Related Report
      2015 Research-status Report
  • [Journal Article] L∞-stability of Discontinuous Traveling Waves in a Hyperbolic-elliptic Coupled System2016

    • Author(s)
      Masashi Ohnawa
    • Journal Title

      SIAM Journal on Mathematical Analysis

      Volume: 48 Issue: 6 Pages: 3820-3839

    • DOI

      10.1137/16m106738x

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] GENERIC formalism and discrete variational derivative method for the two-dimensional vorticity equation2016

    • Author(s)
      Yukihito Suzuki, Masashi Ohnawa
    • Journal Title

      Journal of Computational and Applied Mathematics

      Volume: 296 Pages: 690-708

    • DOI

      10.1016/j.cam.2015.10.018

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Effects of Fluid-Boundary Interaction on the Stability of Boundary Layers in Plasma Physics2016

    • Author(s)
      Masashi Ohnawa
    • Journal Title

      Recent Developments of Mathematical Fluid Mechanics

      Volume: 2016 Pages: 401-410

    • DOI

      10.1007/978-3-0348-0939-9_21

    • ISBN
      9783034809382, 9783034809399
    • Related Report
      2015 Research-status Report
    • Peer Reviewed
  • [Journal Article] Asymptotic stability of plasma boundary layers to the Euler-Poisson equations with fluid-boundary interaction2015

    • Author(s)
      Masashi Ohnawa
    • Journal Title

      SIAM Journal on Mathematical Analysis

      Volume: 47(4) Issue: 4 Pages: 2795-2831

    • DOI

      10.1137/140972019

    • Related Report
      2015 Research-status Report 2014 Research-status Report
    • Peer Reviewed
  • [Journal Article] The mathematical justification of the Bohm criterion in plasma physics2015

    • Author(s)
      Shinya Nishibata, Masashi Ohnawa, Masahiro Suzuki
    • Journal Title

      Advanced Studies in Pure Mathematics

      Volume: 64 Pages: 489-495

    • Related Report
      2015 Research-status Report
    • Peer Reviewed
  • [Journal Article] Existence and uniqueness of solutions to stochastic Rayleigh-Plesset equations2015

    • Author(s)
      T. Funaki, M. Ohnawa, Y. Suzuki, S. Yokoyama
    • Journal Title

      . Math. Anal. Appl.

      Volume: 425 Issue: 1 Pages: 20-32

    • DOI

      10.1016/j.jmaa.2014.12.018

    • Related Report
      2014 Research-status Report
    • Peer Reviewed
  • [Journal Article] $L^\infty$-stability of continuous shock waves in a radiating gas model2014

    • Author(s)
      M. Ohnawa
    • Journal Title

      SIAM J. Math. Anal.

      Volume: 46 Issue: 3 Pages: 2136-2159

    • DOI

      10.1137/130935252

    • Related Report
      2014 Research-status Report
    • Peer Reviewed
  • [Presentation] 輻射気体の衝撃波形態と安定化機構の関係2016

    • Author(s)
      大縄将史
    • Organizer
      Interaction between Pure and Applied Mathematics 2016
    • Place of Presentation
      東京
    • Year and Date
      2016-12-15
    • Related Report
      2016 Annual Research Report
    • Invited
  • [Presentation] On a relation between shock profiles and stabilization mechanisms in a hyperbolic-elliptic coupled system2016

    • Author(s)
      Masashi Ohnawa
    • Organizer
      XVI International Conference on Hyperbolic Problems : Theory, Numerics, Applications
    • Place of Presentation
      Aachen, Germany
    • Year and Date
      2016-08-01
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Existence and stability of shock waves in the Rosenau model2016

    • Author(s)
      Masashi Ohnawa
    • Organizer
      The 8th Nagoya Workshop on Differential Equations
    • Place of Presentation
      名古屋大学
    • Year and Date
      2016-02-23
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] 輻射気体における衝撃波形態の安定化機構による特徴づけ2015

    • Author(s)
      大縄将史
    • Organizer
      京都大学NLPDEセミナー
    • Place of Presentation
      京都大学
    • Year and Date
      2015-11-20
    • Related Report
      2015 Research-status Report
    • Invited
  • [Presentation] 輻射気体における衝撃波の形態と安定化機構の関係2015

    • Author(s)
      大縄将史
    • Organizer
      応用解析研究会
    • Place of Presentation
      早稲田大学
    • Year and Date
      2015-10-24
    • Related Report
      2015 Research-status Report
    • Invited
  • [Presentation] L∞-stability of traveling waves to a hyperbolic-elliptic coupled system2015

    • Author(s)
      Masashi Ohnawa
    • Organizer
      Equadiff 2015
    • Place of Presentation
      Université Claude Bernard Lyon 1, France
    • Year and Date
      2015-07-06 – 2015-07-10
    • Related Report
      2014 Research-status Report
  • [Presentation] L∞-stability of traveling waves to a hyperbolic-elliptic coupled system2015

    • Author(s)
      Masashi Ohnawa
    • Organizer
      Equadiff 2015
    • Place of Presentation
      Lyon, France
    • Year and Date
      2015-07-06
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research
  • [Presentation] 輻射気体モデルにおける進行波の連続性と安定化機構の関係2015

    • Author(s)
      大縄将史
    • Organizer
      非線形解析セミナー@大岡山
    • Place of Presentation
      東京工業大学
    • Year and Date
      2015-06-19
    • Related Report
      2015 Research-status Report
    • Invited
  • [Presentation] A discrete gradient method for the Rayleigh-Plesset-Keller equation2014

    • Author(s)
      I. Oikawa, M. Ohnawa, and Y. Suzuki
    • Organizer
      International Conference on Mathematical Fluid Dynamics
    • Place of Presentation
      早稲田大学
    • Year and Date
      2014-11-11 – 2014-11-14
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] ある双曲型楕円型連立系における衝撃波の形態と安定化機構の関係2014

    • Author(s)
      大縄将史
    • Organizer
      第63 回理論応用力学講演会
    • Place of Presentation
      東京工業大学大岡山キャンパス
    • Year and Date
      2014-09-26 – 2014-09-28
    • Related Report
      2014 Research-status Report
  • [Presentation] 輻射気体における進行波の形態と安定化機構の関係2014

    • Author(s)
      大縄将史
    • Organizer
      日本流体力学会年会2014
    • Place of Presentation
      東北大学 川内北キャンパス
    • Year and Date
      2014-09-15 – 2014-09-17
    • Related Report
      2014 Research-status Report
  • [Presentation] 現代数学解析による流体工学の問題への挑戦2014

    • Author(s)
      柴田良弘,大縄将史
    • Organizer
      第64回熊本大学工学部プロジェクトX講演会
    • Place of Presentation
      熊本大学
    • Year and Date
      2014-06-20
    • Related Report
      2014 Research-status Report
    • Invited
  • [Book] Springer Proceedings in Mathematics and Statistics2017

    • Author(s)
      Masashi Ohnawa
    • Total Pages
      12
    • Publisher
      Springer
    • Related Report
      2016 Annual Research Report
  • [Book] Springer Proceedings in Mathematics and Statics, Vol. 1832016

    • Author(s)
      Masashi Ohnawa
    • Total Pages
      12
    • Publisher
      Springer, Tokyo
    • Related Report
      2016 Annual Research Report
  • [Remarks] 東京海洋大学 海洋環境学科 環境システム科学講座

    • URL

      http://www.s.kaiyodai.ac.jp/kankyoHP/kankyo.html

    • Related Report
      2015 Research-status Report
  • [Remarks] 早稲田大学 重点領域研究機構 非線形偏微分方程式研究所 研究業績 2014年度

    • URL

      http://www.pde.sci.waseda.ac.jp/lab/Work/Work2014.pdf

    • Related Report
      2014 Research-status Report

URL: 

Published: 2014-04-04   Modified: 2022-02-16  

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