The asymptotic stability of one-dimensional linear Bresse systems under infinite memories was proved by Guesmia and Kafini (Math Methods Appl Sci 38:2389–2402, 2015) under three infinite memories, Guesmia and Kirane… Click to show full abstract
The asymptotic stability of one-dimensional linear Bresse systems under infinite memories was proved by Guesmia and Kafini (Math Methods Appl Sci 38:2389–2402, 2015) under three infinite memories, Guesmia and Kirane (Z Angew Math Phys 67:1–39, 2016) under two infinite memories, and De Lima Santos et al. (Q Appl Math 73:23–54, 2015) under one infinite memory acting on the shear angle displacements. The subject of this paper is to complete these results by proving that the asymptotic stability of Bresse systems holds also under one infinite memory acting on the longitudinal displacements.
               
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