Theoretical and computational decay results for a Bresse system with one infinite memory in the longitudinal displacement

Abstract

<p style='text-indent:20px;'>In this paper, we consider a one-dimensional linear Bresse system with only one infinite memory term acting in the third equation (longitudinal displacements). Under a general condition on the memory kernel (relaxation function), we establish a decay estimate of the energy of the system. Our decay result extends and improves some decay rates obtained in the literature such as the one in [<xref ref-type="bibr" rid="b27">27</xref>], [<xref ref-type="bibr" rid="b4">4</xref>], [<xref ref-type="bibr" rid="b33">33</xref>], [<xref ref-type="bibr" rid="b58">58</xref>] and [<xref ref-type="bibr" rid="b34">34</xref>]. The proof is based on the energy method together with convexity arguments. Numerical simulations are given to illustrate the theoretical decay result.</p>