Robust exponential attractors for Coleman-Gurtin equations with dynamic boundary conditions possessing memory

dc.contributor.authorShomberg, Joseph
dc.date.accessioned2023-06-12T20:49:48Z
dc.date.available2023-06-12T20:49:48Z
dc.date.issued2016-02-10
dc.description.abstractWell-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.departmentMathematics
dc.formatText
dc.format.extent35 pages
dc.format.medium1 file (.pdf)
dc.identifier.citationShomberg, J. L. (2016). Robust exponential attractors for Coleman-Gurtin equations with dynamic boundary conditions possessing memory. <i>Electronic Journal of Differential Equations, 2016</i>(47), pp. 1-35.
dc.identifier.issn1072-6691
dc.identifier.urihttps://hdl.handle.net/10877/16921
dc.language.isoen
dc.publisherTexas State University, Department of Mathematics
dc.rightsAttribution 4.0 International
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.sourceElectronic Journal of Differential Equations, 2016, San Marcos, Texas: Texas State University and University of North Texas.
dc.subjectColeman-Gurtin equation
dc.subjectDynamic boundary conditions
dc.subjectMemory relaxation
dc.subjectExponential attractor
dc.subjectBasin of attraction
dc.subjectGlobal attractor
dc.subjectFinite dimensional dynamics
dc.subjectRobustness
dc.titleRobust exponential attractors for Coleman-Gurtin equations with dynamic boundary conditions possessing memory
dc.typeArticle

Files

Original bundle

Now showing 1 - 1 of 1
Loading...
Thumbnail Image
Name:
shomberg.pdf
Size:
465.65 KB
Format:
Adobe Portable Document Format
Description:

License bundle

Now showing 1 - 1 of 1
No Thumbnail Available
Name:
license.txt
Size:
2.54 KB
Format:
Item-specific license agreed upon to submission
Description: