The transmission of waves over a body composed of two different materials are considered in this paper. One component is a simple elastic part while the other is a viscoelastic component with time-varying delay and damping effect. Besides, one part of the boundary is controlled by a nonlinear memory source term while the other part of the boundary is clamped. Under the influence of time-varying delay and damping effect, we derive a general decay estimate of the energy when the internal viscoelastic memory and the boundary memory decay simultaneously. Moreover, we present some examples to illustrate that the decay rate of the energy is optimal in some range of decay exponent of the memory.

本文考虑了波在由两种不同材料组成的物体上的传输。一种是简单的弹性部件，另一种是具有时变延迟和阻尼作用的粘弹性部件。此外，边界的一部分由非线性记忆源项控制，而边界的另一部分被钳位。在时变延迟和阻尼效应的影响下，我们推导出了内部粘弹性记忆和边界记忆同时衰减时能量的一般衰减估计。此外，我们还举了一些例子来说明能量的衰减率在内存衰减指数的某个范围内是最优的。