The Perturbation Method due to the Small Change in the Shape of the Boundary

スポンサーリンク

概要

• 論文の詳細を見る

• A general method is presented for estimating the effect caused by a small change in the boundary shape (or the hypersurface shape in the many-dimensional space, the time-coordinate being included) upon the solutions or eigenvalues of linear partial differential equations (elliptic, parabolic or hyperbolic). When the given boundary is slightly deformed from a shape favorable for obtaining the solutions, this method gives the approximate solutions or eigenvalues based upon the exact or unperturbed ones for the case of the favorable shape, where many solutions can be obtained easier. The following illustrative examples are given, showing the validity of the method presented: (1) The eigenfrequencies of the lateral vibration of a uniform membrane fixed at its boundary close to a circle in shape, e.g. elliptic, oval, cinquefoil-shaped, etc. (2) The eigenvalue problem concerning the heat conduction of a "corned-beef-can" -shaped uniform matter, close to a rectangular parallelepiped in shape and with its temperature being kept constant on the boundary surface. (3) Three boundary-value problems representing the parabolic, hyperbolic and elliptic cases, respectively.

• 社団法人日本物理学会の論文
• 1960-11-05

著者

• Saito Tomoyuki

  Tokyo University Of Agriculture And Technology:tokyo Noko Daigaku

• Saito Tomoyuki

  Tokyo University Of Agriculture And Technology

• Saito T.

  Tokyo University of Agriculture and Technology:Tokyo Noko Daigaku

関連論文

• The Boundary-Perturbation Method for Tensor-Fie1ds
• The Perturbation Method due to the Small Change in the Shape of the Boundary
• The W.K.B. Method for the Differential Equations of the Fourth Order
• The Modulation in a Cylindrical Cavity-Resonator by Its Small Time-Dependent Deformation

スポンサーリンク