Existence and uniqueness for a viscoelastic Kelvin–Voigt model with nonconvex stored energy

Konstantinos Koumatos, Corrado Lattanzio, Stefano Spirito, Athanasios Tzavaras

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

We consider nonlinear viscoelastic materials of Kelvin–Voigt-type with stored energies satisfying an Andrews–Ball condition, allowing for nonconvexity in a compact set. Existence of weak solutions with deformation gradients in [Formula: see text] 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.
Original languageEnglish (US)
Pages (from-to)433-474
Number of pages42
JournalJournal of Hyperbolic Differential Equations
Volume20
Issue number02
DOIs
StatePublished - Aug 8 2023

Bibliographical note

KAUST Repository Item: Exported on 2023-09-07
Acknowledgements: Corrado  Lattanzio  and  Stefano  Spirito  are  partially  supported  by  the  GruppoNazionale  per   l’Analisi  Matematica,  la  Probabilit`a  e   le  loro  Applicazioni(GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM), and by thePRIN 2020 Non-linear evolution PDEs, fluid dynamics and transport equations:theoretical foundations and applications.

ASJC Scopus subject areas

  • Analysis
  • General Mathematics

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