| Autor: |
Joseph L. Shomberg |
| Jazyk: |
angličtina |
| Rok vydání: |
2016 |
| Předmět: |
|
| Zdroj: |
Electronic Journal of Differential Equations, Vol 2016, Iss 47,, Pp 1-35 (2016) |
| Druh dokumentu: |
article |
| ISSN: |
1072-6691 |
| Popis: |
Well-posedness of generalized Coleman-Gurtin equations equipped with dynamic boundary conditions with memory was recently established by the author with C. G. Gal. In this article we report advances concerning the asymptotic behavior and stability of this heat transfer model. For the model under consideration, we obtain a family of exponential attractors that is robustHolder continuous with respect to a perturbation parameter occurring in a singularly perturbed memory kernel. We show that the basin of attraction of these exponential attractors is the entire phase space. The existence of (finite dimensional) global attractors follows. The results are obtained by assuming the nonlinear terms defined on the interior of the domain and on the boundary satisfy standard dissipation assumptions. Also, we work under a crucial assumption that dictates the memory response in the interior of the domain matches that on the boundary. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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