波动方程在半无穷柱体和外部区域上的空间爆破和衰减性

Spatial Blow up and Decay of Wave Equationin onSemi-infinite Cylinder and Exterior Region

利用能量分析的方法,首先考虑定义在三维半无穷柱体上的波动方程,当空间变量趋于无穷时,证明其解或者指数式增长或者指数式衰减;其次,考虑定义在球面外部区域上的波动方程,证明其解随半径的二择一结果;最后,证明对于非线性弹性方程,二择性定理仍有效.

By using the method of energy analysis,firstly,we considered the wave equation defined on a three-dimensional semi-infinite cylinde r.When the spatial variable approached infinity,we proved that the solution of the equation either grew exponentially or decayed exponentially.Secondly,we c onsidered the wave equation defined on the exterior region of the sphere,and proved the alternative result of its solution with radius.Finally,we proved that the alternative theorem was still valid for nonlinear elastic equations.