Asymptotic behavior and singular limit problem for dissipative hyperbolic equations

• Project/Area Number: 21540201
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Tokyo University of Science
• Principal Investigator: YAMAZAKI Taeko 東京理科大学, 理工学部, 教授 (60220315)
• Project Period (FY): 2009 – 2011
• Project Status: Completed (Fiscal Year 2011)
• Budget Amount: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000); Fiscal Year 2011: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2010: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2009: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
• Keywords: Kirchhhoff方程式 / 消散型双曲型方程式 / Kirchhiff型方程式 / Kirchhoff方程式 / 消散項 / 漸近挙動 / 大域解

Research Abstract

We considered dissipative Kirchhoff equation with dissipation, where the coefficient of the dissipation decays with respect to the time valuable. First we consider dissipative Kirchhoff equation where the coefficient of the dissipation term depends time and space valuables and decays slowly than the critical exponent with respect to the time valuable. Then we proved the unique global existence of the solution for initial data with small Sobolev norm. Secondly we considered the dissipative Kirchhoff equation where the coefficient of the dissipation term depends only on time valuable which decays rapidly. Then we showed the unique global solvability and existence of the scattering on some class of the functions.

Research Products

• [Journal Article] Hyperbolic parabolic singular perturbation for quasilinear equations of Kirchhoff type with weak dissipation (2009)
  • Author(s): Taeko Yamazaki
  • Journal Title: Mathematical Methods in the Applied Sciences 32 Pages: 1893-1918
  • Peer Reviewed