无穷远耗散波导中的能量衰减
Energy Decay in a Wave Guide with Dissipation at Infinity
摘要：
我们证明了局部和整体的能量衰减的波动方程在波导中的阻尼在无穷远。更准确地说，吸收指数被假定为缓慢收敛到一个正常数，我们得到的扩散现象典型的贡献时，在无穷大的阻尼是有效的低频率。另一方面，通常的几何控制条件不一定满足，所以我们可能会失去高频贡献的规律性。由于我们的结果即使在欧氏空间中也是新的，所以在这种情况下我们也陈述一个类似的结果。
英文摘要：
We prove local and global energy decay for the wave equation in a wave guide with damping at infinity. More precisely, the absorption index is assumed to converge slowly to a positive constant, and we obtain the diffusive phenomenon typical for the contribution of low frequencies when the damping is effective at infinity. On the other hand, the usual Geometric Control Condition is not necessarily satisfied so we may have a loss of regularity for the contribution of high frequencies. Since our results are new even in the Euclidean space, we also state a similar result in this case.
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