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

Konstantinos Koumatos; Corrado Lattanzio; Stefano Spirito; Athanasios Tzavaras

doi:10.1142/s0219891623500133

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 journal › Article › peer-review

2 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 language	English (US)
Pages (from-to)	433-474
Number of pages	42
Journal	Journal of Hyperbolic Differential Equations
Volume	20
Issue number	02
DOIs	https://doi.org/10.1142/s0219891623500133
State	Published - 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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10.1142/s0219891623500133

https://repository.kaust.edu.sa/bitstream/10754/666734/5/klst_viscoelasticity.pdf

Cite this

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title = "Existence and uniqueness for a viscoelastic Kelvin–Voigt model with nonconvex stored energy",

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.",

author = "Konstantinos Koumatos and Corrado Lattanzio and Stefano Spirito and Athanasios Tzavaras",

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T1 - Existence and uniqueness for a viscoelastic Kelvin–Voigt model with nonconvex stored energy

AU - Koumatos, Konstantinos

AU - Lattanzio, Corrado

AU - Spirito, Stefano

AU - Tzavaras, Athanasios

N1 - 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.

PY - 2023/8/8

Y1 - 2023/8/8

N2 - 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.

AB - 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.

UR - http://hdl.handle.net/10754/666734

UR - https://www.worldscientific.com/doi/10.1142/S0219891623500133

U2 - 10.1142/s0219891623500133

DO - 10.1142/s0219891623500133

M3 - Article

SN - 0219-8916

VL - 20

SP - 433

EP - 474

JO - Journal of Hyperbolic Differential Equations

JF - Journal of Hyperbolic Differential Equations

IS - 02

ER -

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

Abstract

Bibliographical note

ASJC Scopus subject areas

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