耗散波导中的局域能量衰减和扩散现象
Local Energy Decay and Diffusive Phenomenon in a Dissipative Wave Guide
摘要：
本文证明了边界有耗散的波导中波动方程的局部能量衰减。看来，对于大的时间耗散波的行为就像一个解决方案的热方程在无界方向。证明是基于预解估计。由于横向算子的本征向量不形成Riesz基，谱分析并不简单地简化为紧域和欧氏域上的单独分析。
英文摘要：
We prove the local energy decay for the wave equation in a wave guide with dissipation at the boundary. It appears that for large times the dissipated wave behaves like a solution of a heat equation in the unbounded directions. The proof is based on resolvent estimates. Since the eigenvectors for the transverse operator do not form a Riesz basis, the spectral analysis does not trivially reduce to separate analyses on compact and Euclidean domains.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
