Uniform Stability of the Solution for a Memory-Type Elasticity System with Nonhomogeneous Boundary Control Condition

In this paper, we consider the memory-type elasticity system \(\boldsymbol {u}_{tt}-\upmu {\Delta }{\boldsymbol {u}}-(\upmu +\lambda )\nabla (\text {div}\boldsymbol {u})+{{\int }^{t}_{0}}g(t-\tau ){\Delta }{\boldsymbol {u}}(s)ds=0,\) with nonhomogeneous boundary control condition and establish the uniform stability result of the solution. The exponential decay result and polynomial decay result in some literature are the special cases of this paper.