具有非线性边界条件的调和方程在无界区域上的Phragmén-Lindelof二择性结果

Phragmén-Lindelof Alternative Type Results for the Harmonic Equation with Nonlinear Boundary Conditions in an Unbounded Region

考虑了定义在一个半无穷柱体上调和方程的渐近性质,其中在柱体的有限端和侧面上施加了不同的非线性边界条件.定义了一个能量表达式,并得到了关于此能量表达式的二阶微分不等式.通过对3种不同类型的无界区域进行分析,运用微分不等式技术和能量估计的方法,得到了调和方程的二择一结果.在衰减的情形,推导了全能量的显式上界.

By defining an energy expression composed of solutions of harmonic equations,a first order differential inequality on energy is derived by using differential inequality technique.Three different types of cylindrical regions are analyzed,and the solutions of the equations are either exponential growth or exponential decay.In the case of decay,the explicit upper bound of total energy is derived.