Asymptotic stability of abstract dissipative systems with infinite memory |
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Authors: | Aissa Guesmia |
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Institution: | LMAM, Bat. A, Université Paul Verlaine-Metz, Ile du Saulcy, 57045 Metz Cedex 01, France |
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Abstract: | We consider in this paper the problem of asymptotic behavior of solutions to an abstract linear dissipative integrodifferential equation with infinite memory (past history) modeling linear viscoelasticity. We show that the stability of the system holds for a much larger class of the convolution kernels than the one considered in the literature, and we provide a relation between the decay rate of the solutions and the growth of the kernel at infinity. Some applications are also given. |
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Keywords: | Linear viscoelasticity Contraction semigroups Asymptotic behavior Infinite memory kernels |
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