We prove a decay estimate for solutions to a transmission problem for wave equations with different propagation speeds in an infinite waveguide. The problem represents the wave propagation in unbounded and layered composite materials in which different properties are given. It is a new composition of a waveguide problem and a transmission problem, motivated by a unit cell model for CFRP. The proof is based on splitting variables, partial eigenfunction expansions in the bounded cross section, and on an explicit Weyl type estimate for the eigenvalues.

中文翻译：

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无限波导中波动方程的传输问题


我们证明了无限波导中具有不同传播速度的波动方程的传输问题解的衰减估计。该问题表示波在无界和多层复合材料中的传播，其中给出了不同的属性。这是波导问题和传输问题的新组合，由 CFRP 的晶胞模型驱动。该证明基于分裂变量、有界横截面中的部分特征函数展开以及特征值的显式 Weyl 类型估计。