Abstract
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.
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