On reconstruction problems in inverse problems of determining unknown coefficients for non-linear partial differential equations

• Project/Area Number: 20740078
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Basic analysis
• Research Institution: Tokyo University of Science
• Principal Investigator: WATANABE Michiyuki Tokyo University of Science, 人文社会・教育科学系, 准教授 (90374181)
• Project Period (FY): 2008 – 2010
• Project Status: Completed (Fiscal Year 2010)
• Budget Amount: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000); Fiscal Year 2010: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2009: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2008: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
• Keywords: 偏微分方程式 / 散乱理論 / 逆問題

Research Abstract

(1) We give the existence of outgoing eigen-function and its scattering amplitude for the two dimensional stationary wave equation with a friction term. We also prove in two dimensions that the friction coefficient is uniquely reconstructed from the scattering amplitude at a fixed low energy. (2) We study the inverse boundary value problem of determining a field-dependent coefficient for the non-linear wave equation in one space dimension. We prove that a linear part and a quadratic part of the field-dependent coefficient are uniquely reconstructed from the boundary measurements.

Research Products

• [Journal Article] Two-dimensional inverse problem for Schrodinger equation with a complex coefficient (2010)
  • Author(s): 渡邊道之
  • Journal Title: 数理解析研究所講究録別 B16巻 Pages: 175-194
  • Peer Reviewed
• [Journal Article] Two-dimensional inverse problem for Schrodinger equation with a complex coefficient (2010)
  • Author(s): 渡邊道之
  • Journal Title: 数理解析研究所講究録別冊 Volume: B16 Pages: 175-194
  • Peer Reviewed
• [Journal Article] On inverse boundary value problems for the two dimensional Schrodinger equation with complex-valued potentials (in Japanese) (2009)
  • Author(s): 渡邊道之
  • Journal Title: Seminar Notes of Mathematical Sciences 12巻 Pages: 216-224
• [Journal Article] Barbara KaltenbacherOn、the identification of a coefficient function in a nonlinear wave equation (2009)
  • Author(s): 中村玄、渡邊道之
  • Journal Title: INVERSE PROBLEMS Vol.25
  • Peer Reviewed
• [Journal Article] On inverse boundary value problems for the two dimensional Schrodinger equation with complex-valued potentials (in Japanese) (2009)
  • Author(s): 渡邊道之
  • Journal Title: Senubar Notes of Mathematical Sciences 12 Pages: 216-224
• [Presentation] Inverse scattering problem for stationary wave equation with a friction term in two dimensions (2009)
  • Author(s): 渡邊道之
  • Organizer: International Conference on Inverse Problems and Applications
  • Place of Presentation: Hanbat National University、Daejeon、Korea
  • Year and Date: 2009-08-17
• [Presentation] Inverse scattering problem for stationary wave equation with a friction term in two dimensions (2009)
  • Author(s): 渡邊道之
  • Organizer: International Conference on Inverse Problems and Applications
  • Place of Presentation: Hanbat National University, Daejeon, Korea
  • Year and Date: 2009-08-17
• [Presentation] 複素ポテンシャルをもつシュレーディンガー方程式の境界値逆問題 (2008)
  • Author(s): 渡邊道之
  • Organizer: 日本数学会
  • Place of Presentation: 東京工業大学
  • Year and Date: 2008-09-26
• [Presentation] 複素ポテンシャルをもつシュレーディンガー方程式の境界値逆問題 (2008)
  • Author(s): 渡邊道之
  • Organizer: 日本数学会2008年度秋季総合分科会函数方程式論分科会
  • Place of Presentation: 東京工業大学
  • Year and Date: 2008-09-26