临界情况下圆柱形势阱的散射
On Scattering by a Cylindrical Trap in Critical Case
摘要：
我们考虑一个二维模拟的亥姆霍兹共振器的壁的有限厚度的临界情况下，当存在一个本征频率等于限制的极点产生的有界组件的谐振器和狭窄的连接通道。在极限本征频率为有界分量的简单本征频率的假设下，利用匹配渐近展开法构造了收敛于该本征频率的两个极点的渐近性。得到了极点渐近的主导项和散射问题解的显式表达式。
英文摘要：
We consider a two-dimensional analogue of Helmholtz resonator with walls of finite thickness in the critical case when there exists an eigenfrequency equalling to the limit of poles generated by both the bounded component of the resonator and by the narrow connecting channel. Under assumption that the limit eigenfrequency is simple one of the bounded component, asymptotics of two poles converging to this eigenfrequency are constructed by using the method of matching asymptotic expansions. The explicit formulas for the leading terms of asymptotics for poles and for the solution of the scattering problem are obtained.
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