Asymptotic stability of abstract dissipative systems with infinite memory
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 kern...
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| Veröffentlicht in: | Journal of mathematical analysis and applications 2011-10, Vol.382 (2), p.748-760 |
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| container_title | Journal of mathematical analysis and applications |
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| creator | Guesmia, Aissa |
| description | 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. |
| doi_str_mv | 10.1016/j.jmaa.2011.04.079 |
| format | Article |
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| language | eng |
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| source | Elsevier ScienceDirect Journals; Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals |
| subjects | Analysis of PDEs Asymptotic behavior Contraction semigroups Exact sciences and technology Global analysis, analysis on manifolds Group theory Group theory and generalizations Infinite memory kernels Integral equations Linear viscoelasticity Mathematical analysis Mathematics Sciences and techniques of general use Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds |
| title | Asymptotic stability of abstract dissipative systems with infinite memory |
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