Qualitative properties for the Laplace equation with a dynamical boundary condition

• Project/Area Number: 23654060
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• Research Field: Global analysis
• Research Institution: Tohoku University
• Principal Investigator: ISHIGE Kazuhiro 東北大学, 大学院・理学研究科, 教授 (90272020)
• Project Period (FY): 2011 – 2012
• Project Status: Completed (Fiscal Year 2012)
• Budget Amount: ¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000); Fiscal Year 2012: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000); Fiscal Year 2011: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
• Keywords: 動的境界条件 / ラプラス方程式 / ポアソン核 / 藤田臨界指数 / 大域挙動

Research Abstract

We studied the large time behavior of positive solutions for the Laplace equation with a nonlinear dynamical boundary condition and for a nonlinear elliptic equation with a dynamical boundary condition, in a half space. We identified a critical exponent for the global existence of positive solutions and showed that small solutions behave likesuitable multiples of the Poisson kernel.

Research Products

• [Journal Article] Large time behavior of solutions of a semilinear elliptic equation with a dynamical boundary condition (2013)
  • Author(s): Marek Fila、Kazuhiro Ishige,、Tatsuki Kawakami
  • Journal Title: Advances in Differential Equations Volume: 18巻 Pages: 69-100
  • Peer Reviewed
• [Journal Article] Large time behavior of solutions of a semilinear elliptic equation with a dynamical boundary condition (2013)
  • Author(s): M. Fila, K. Ishige, and T. Kawakami
  • Journal Title: Adv. Differential Equations Volume: 18
  • Peer Reviewed
• [Journal Article] Convergence to the Poisson kernel for the Laplace equation with a nonlinear dynamical boundary condition (2012)
  • Author(s): M. Fila, K. Ishige, and T. Kawakami
  • Journal Title: Commun. Pure Appl. Anal. Volume: 11 Issue: 3 Pages: 1285-1301
  • DOI: 10.3934/cpaa.2012.11.1285
  • Peer Reviewed
• [Journal Article] Convergence to the Poisson kernel for the Laplace equation with a nonlinear dynamical boundary condition (2012)
  • Author(s): M. Fila, K. Ishige, and T. Kawakami
  • Journal Title: Commun. Pure Appl. Anal. Volume: 11
  • Peer Reviewed