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Existence and uniqueness for a viscoelastic Kelvin-Voigt model with nonconvex stored energy
journal contribution
posted on 2023-06-10, 06:44 authored by Konstantinos KoumatosKonstantinos Koumatos, Athanasios Tzavaras, Stefano Spirito, Corrado LattanzioWe consider nonlinear viscoelastic materials of Kelvin-Voigt type with stored energies satisfying an Andrews-Ball condition, allowing for non convexity in a compact set. Existence of weak solutions with deformation gradients in H1 is established for energies of any superquadratic growth. In two space dimensions, weak solutions notably turn out to be unique in this class. Conservation of energy for weak solutions in two and three dimensions, as well as global regularity for smooth initial data in two dimensions are established under additional mild restrictions on the growth of the stored energy.
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- Published
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- Accepted version
Journal
Journal of Hyperbolic Differential EquationsISSN
0219-8916Publisher
World ScientificPublisher URL
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Issue
2Volume
20Pages
433-474Department affiliated with
- Mathematics Publications
Full text available
- No
Peer reviewed?
- Yes
Legacy Posted Date
2023-04-14First Compliant Deposit (FCD) Date
2023-04-14Usage metrics
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