Robust exponential attractors for Coleman-Gurtin equations with dynamic boundary conditions possessing memory
| dc.contributor.author | Shomberg, Joseph | |
| dc.date.accessioned | 2023-06-12T20:49:48Z | |
| dc.date.available | 2023-06-12T20:49:48Z | |
| dc.date.issued | 2016-02-10 | |
| dc.description.abstract | 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 robust/Hölder 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. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 35 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Shomberg, J. L. (2016). Robust exponential attractors for Coleman-Gurtin equations with dynamic boundary conditions possessing memory. Electronic Journal of Differential Equations, 2016(47), pp. 1-35. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/16921 | |
| dc.language.iso | en | |
| dc.publisher | Texas State University, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 2016, San Marcos, Texas: Texas State University and University of North Texas. | |
| dc.subject | Coleman-Gurtin equation | |
| dc.subject | Dynamic boundary conditions | |
| dc.subject | Memory relaxation | |
| dc.subject | Exponential attractor | |
| dc.subject | Basin of attraction | |
| dc.subject | Global attractor | |
| dc.subject | Finite dimensional dynamics | |
| dc.subject | Robustness | |
| dc.title | Robust exponential attractors for Coleman-Gurtin equations with dynamic boundary conditions possessing memory | |
| dc.type | Article |