Large-time behavior of solutions to the drift-diffusion equation

• Project/Area Number: 23740117
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Global analysis
• Research Institution: Hirosaki University
• Principal Investigator: MASAKAZU Yamamoto 弘前大学, 理工学研究科, 助教 (00600066)
• Project Period (FY): 2011-04-28 – 2015-03-31
• Project Status: Completed (Fiscal Year 2014)
• Budget Amount: ¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000); Fiscal Year 2014: ¥130,000 (Direct Cost: ¥100,000、Indirect Cost: ¥30,000); Fiscal Year 2013: ¥520,000 (Direct Cost: ¥400,000、Indirect Cost: ¥120,000); Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
• Keywords: 関数方程式 / 関数解析 / 実解析 / 応用数学

Outline of Final Research Achievements

In this plan, we developed the asymptotic expansion of solutions to the drift-diffusion equation which is described from the model of a semiconductor. Since an electron on a semiconductor may jump from a dopant into another, the dissipation of them is written by the fractional Laplacian. We proved that the asymptotic expansion

Research Products

• [Journal Article] Local and global solvability and blow up for the drift-diffusion equation with the fractional dissipation with the critical space (2015)
  • Author(s): Sugiyama, Y., Yamamoto, M., Kato, K.
  • Journal Title: Journal of Differential Equations Volume: 258 Issue: 9 Pages: 2983-3010
  • DOI: 10.1016/j.jde.2014.12.033
  • Peer Reviewed
• [Journal Article] Asymptotic expansion of solutions to the nonlinear dissipative equation with the anomalous diffusion (2015)
  • Author(s): Yamamoto, M.
  • Journal Title: Journal of Mathematical Analysis and Applications Volume: 427 Issue: 2 Pages: 1027-1069
  • DOI: 10.1016/j.jmaa.2015.02.025
  • Peer Reviewed
• [Journal Article] Existence and analyticity of solutions to the drift-diffusion equation with critical dissipation (2014)
  • Author(s): Yamamoto, M., Kato, K., Sugiyama, Y.,
  • Journal Title: Hiroshima Mathematical Journal Volume: 44 Pages: 275-313
  • Peer Reviewed
• [Journal Article] Asymptotic stability of stationary solutions to the drift-diffusion model in the whole space (2012)
  • Author(s): R. Kobayashi
  • Journal Title: ESAIM: Control, Optimisation and Calculus of Variations Volume: 18 Issue: 4 Pages: 1097-1121
  • DOI: 10.1051/cocv/2011191
  • Peer Reviewed
• [Journal Article] Large-time behavior of solutions to the drift-diffusion equation with fractional dissipation (2012)
  • Author(s): Yamamoto, M.
  • Journal Title: Differential Integral Equations Volume: 25 Pages: 731-758
  • Peer Reviewed
• [Journal Article] Asymptotic expansion of solutions to the dissipative equation with fractional Laplacian (2012)
  • Author(s): Yamamoto, M.
  • Journal Title: SIAM J. Math. Anal. Volume: 44 Issue: 6 Pages: 3786-3805
  • DOI: 10.1137/120873200
  • Peer Reviewed
• [Journal Article] Spatial analyticity of solutions to the drift-diffusion equation with generalized dissipation (2011)
  • Author(s): Yamamoto, M.
  • Journal Title: Arch. Math. Volume: 97 Issue: 3 Pages: 261-270
  • DOI: 10.1007/s00013-011-0302-x
  • Peer Reviewed
• [Presentation] 臨界型移流拡散方程式の解の時間大域挙動について (2015)
  • Author(s): 山本征法
  • Organizer: 常微分方程式ワークショップ 松山 2015
  • Place of Presentation: 愛媛大学
  • Year and Date: 2015-03-10
  • Invited
• [Presentation] Asymptotic behavior of solutions to the drift-diffusion equation of elliptic type (2014)
  • Author(s): 山本征法
  • Organizer: 抽象発展方程式理論から見た偏微分方程式に関する評価方法の再考
  • Place of Presentation: 数理解析研究所
  • Year and Date: 2014-10-22 – 2014-10-24
  • Invited
• [Presentation] 臨界拡散を持つ移流拡散方程式の解の漸近挙動について (2014)
  • Author(s): 山本征法
  • Organizer: 第4回 室蘭非線形解析研究会
  • Place of Presentation: 室蘭工業大学
  • Year and Date: 2014-10-17 – 2014-10-18
  • Invited
• [Presentation] 臨界拡散を持つ移流拡散方程式の解の挙動について (2014)
  • Author(s): 山本征法
  • Organizer: 日本数学会2014年度秋季総合分科会
  • Place of Presentation: 広島大学
  • Year and Date: 2014-09-25 – 2014-09-28
• [Presentation] Asymptotic profile of solutions to the drift-diffusion equation with critical dissipation (2014)
  • Author(s): 山本征法
  • Organizer: 第127回 神楽坂解析セミナー
  • Place of Presentation: 東京理科大学
  • Year and Date: 2014-09-06
  • Invited
• [Presentation] Asymptotic expansion of solutions to the drift-diffusion equation with critical dissipation (2014)
  • Author(s): Yamamoto, M.
  • Organizer: The 10th AIMS Conference on Dynamical Systems, Differential Equations and Applications
  • Place of Presentation: Autonomous University of Madrid, Madrid, Spain
• [Presentation] Asymptotic expansion of solutions to the dissipative equation with fractional dissipation (2013)
  • Author(s): Yamamoto, M.
  • Organizer: Equadiff13
  • Place of Presentation: Charles University in Prague, Prague, Czech Republic
• [Presentation] 特異拡散を持つ移流拡散方程式の解の挙動について (2013)
  • Author(s): 山本征法
  • Organizer: 日本数学会2013年度秋季総合分科会
  • Place of Presentation: 愛媛大学
• [Presentation] Asymptotic expansion of solutions to the dissipative equation with anomalous diffusion (2012)
  • Author(s): Yamamoto, M.
  • Organizer: The 37th Sapporo Symposium on Partial Differential Equations
  • Place of Presentation: Hokkaido University
  • Invited
• [Presentation] 分数冪ラプラシアンの拡散方程式の解の挙動について (2012)
  • Author(s): 山本征法
  • Organizer: 日本数学会2012年度秋季総合分科会
  • Place of Presentation: 九州大学
• [Presentation] 移流拡散方程式の解の漸近形の特殊な場合について (2012)
  • Author(s): 山本 征法
  • Organizer: 愛媛大学数学談話会(招待講演)
  • Place of Presentation: 愛媛大学理学部
• [Presentation] 非局所的な拡散効果をもつ移流拡散方程式の解の時間大域挙動について (2011)
  • Author(s): 山本 征法
  • Organizer: NLPDEセミナー(招待講演)
  • Place of Presentation: 京都大学大学院理学研究科
• [Presentation] Large-time behavior of solutions to the drift-diffusion equation (2011)
  • Author(s): Yamamoto, M.
  • Organizer: The 4th MSJ-SI Nonlinear Dynamics in Partial Differential Equations
  • Place of Presentation: Kyushu University
• [Presentation] 拡散効果を一般化した移流拡散方程式の解の漸近挙動について (2011)
  • Author(s): 山本 征法
  • Organizer: 日本 数学会 2011 年度秋季総合分科会
  • Place of Presentation: 信州大学