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Asymptotic stability of semigroups associated with linear weak dissipative systems with memory |
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| Authors: | Jaime E Muñoz Rivera Maria Grazia Naso |
| Institution: | a National Laboratory for Scientific Computation, Rua Getulio Vargas 333, Quitadinha-Petrópolis 25651-070, Rio de Janeiro, RJ, Brazil b Dipartimento di Matematica, Facoltà di Ingegneria, Università degli Studi di Brescia, Via Valotti 9, 25133 Brescia, Italy |
| Abstract: | We study the asymptotic behavior of the solutions of a class of linear dissipative integral differential equations. We show in the abstract setting a necessary and sufficient condition to get an exponential decay of the solution. In the case of the lack of exponential decay, we find the polynomial rate of decay of the solution. Some examples are given. |
| Keywords: | Materials with memory Asymptotic stability Semigroups |
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