- Library Home /
- Search Collections /
- Open Collections /
- Browse Collections /
- BIRS Workshop Lecture Videos /
- Existence and uniqueness for a viscoelastic Kelvin-Voigt...
Open Collections
BIRS Workshop Lecture Videos
BIRS Workshop Lecture Videos
Existence and uniqueness for a viscoelastic Kelvin-Voigt model with nonconvex stored energy Tzavaras, Athanasios
Description
We consider the Kelvin-Voigt model for viscoelasticity and prove propagation of $H^1$-regularity for the deformation gradient of weak solutions in two and three dimensions assuming that the stored energy satisfies the Andrews-Ball condition, in particular allowing for a non-monotone stress. By contrast, a counterexample indicates that for non-monotone stress-strain relations (even in 1-d) initial oscillations
of the strain lead to solutions with sustained oscllations. In addition, in two space dimensions, we prove that the weak solutions with deformation gradient in $H^1$ are in fact unique, providing a striking analogy to the 2D Euler equations with bounded vorticity. (joint work with K. Koumatos (U. of Sussex), C. Lattanzio and S. Spirito (U. of Lâ Aquila)).
Item Metadata
| Title |
Existence and uniqueness for a viscoelastic Kelvin-Voigt model with nonconvex stored energy
|
| Creator | |
| Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
|
| Date Issued |
2020-11-27T10:29
|
| Description |
We consider the Kelvin-Voigt model for viscoelasticity and prove propagation of $H^1$-regularity for the deformation gradient of weak solutions in two and three dimensions assuming that the stored energy satisfies the Andrews-Ball condition, in particular allowing for a non-monotone stress. By contrast, a counterexample indicates that for non-monotone stress-strain relations (even in 1-d) initial oscillations
of the strain lead to solutions with sustained oscllations. In addition, in two space dimensions, we prove that the weak solutions with deformation gradient in $H^1$ are in fact unique, providing a striking analogy to the 2D Euler equations with bounded vorticity. (joint work with K. Koumatos (U. of Sussex), C. Lattanzio and S. Spirito (U. of Lâ Aquila)).
|
| Extent |
20.0 minutes
|
| Subject | |
| Type | |
| File Format |
video/mp4
|
| Language |
eng
|
| Notes |
Author affiliation: KAUST
|
| Series | |
| Date Available |
2021-05-27
|
| Provider |
Vancouver : University of British Columbia Library
|
| Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
|
| DOI |
10.14288/1.0398186
|
| URI | |
| Affiliation | |
| Peer Review Status |
Unreviewed
|
| Scholarly Level |
Faculty
|
| Rights URI | |
| Aggregated Source Repository |
DSpace
|
Item Media
Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International