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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. </p>
(joint work with K. Koumatos (U. of Sussex), C. Lattanzio and S. Spirito (U. of Lâ Aquila)). </p>
Item Metadata
Title |
Existence and uniqueness for a viscoelastic Kelvin-Voigt model with nonconvex stored energy
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Creator | |
Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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Date Issued |
2020-11-27T10:29
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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. </p> (joint work with K. Koumatos (U. of Sussex), C. Lattanzio and S. Spirito (U. of Lâ Aquila)). </p> |
Extent |
20.0 minutes
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Subject | |
Type | |
File Format |
video/mp4
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Language |
eng
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Notes |
Author affiliation: KAUST
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Series | |
Date Available |
2021-05-27
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Provider |
Vancouver : University of British Columbia Library
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Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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DOI |
10.14288/1.0398186
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URI | |
Affiliation | |
Peer Review Status |
Unreviewed
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Scholarly Level |
Faculty
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Rights URI | |
Aggregated Source Repository |
DSpace
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Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International