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

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Abstract

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.

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Authors and Affiliations

  1. School of Mathematical Sciences, Qufu Normal University, Qufu, 273165, People’s Republic of China

    Fushan Li & Yuping Bao

Authors
  1. Fushan Li
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  2. Yuping Bao
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Correspondence to Fushan Li.

Additional information

This work was supported by the National Natural Science Foundation of China (11201258), the Natural Science Foundation of Shandong Province (ZR2011AM008, ZR2011AQ006, ZR2012AM010) and the Program for Scientific research innovation team in Colleges and universities of Shandong Province.

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Li, F., Bao, Y. Uniform Stability of the Solution for a Memory-Type Elasticity System with Nonhomogeneous Boundary Control Condition. J Dyn Control Syst 23, 301–315 (2017). https://doi.org/10.1007/s10883-016-9320-0

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  • DOI: https://doi.org/10.1007/s10883-016-9320-0

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