标题： 关于临界情况下圆柱形陷阱的散射 显示英文标题

标题： On Scattering by a Cylindrical Trap in Critical Case

摘要： 我们考虑一个二维的赫姆霍兹谐振器的类似物，其壁具有有限厚度，在临界情况下，存在一个特征频率等于由谐振器的有限部分和狭窄连接通道产生的极点的极限。 在假设极限特征频率是有限部分的一个简单特征频率的情况下，通过使用匹配渐近展开的方法，构造了两个收敛到该特征频率的极点的渐近表达式。 得到了极点和散射问题解的渐近表达式的主导项的显式公式。 显示英文摘要

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.