三维柱体上调和方程的二择一结果
Phragmén-Lindel?f Alternative Type Results for Harmonic Equation in A 3D Cylinder
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摘要: 通过定义一个由调和方程的解组成的能量表达式,运用微分不等式技术,推导出了一个关于能量的一阶微分不等式.对3种不同类型的柱形区域进行分析,得到了方程的解要么呈指数式增长要么呈指数式衰减.在衰减的情形,推到了全能量的显式上界.Abstract: In the report, by defining an energy expression composed of solutions of harmonic equations, the differential inequality technique was used to derive a first order differential inequality on energy. Three different types of cylindrical regions were analyzed. The results showed that the solutions of the equations are either exponential growth or exponential decay. In the case of decay, the explicit upper bound of total energy was derived.
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