papers

Publications (8)

math.AP2023

Non-isothermal multicomponent flows with mass diffusion and heat conduction

Stefanos Georgiadis, Ansgar Jüngel, Athanasios Tzavaras

A type-I model of non-isothermal multicomponent systems of gases describing mass diffusive and heat conductive phenomena is presented. The derivation of the model and a convergence…

math.AP2016

Existence of localizing solutions in plasticity via geometric singular perturbation theory

Min-Gi Lee, Athanasios Tzavaras

Shear bands are narrow zones of intense shear observed during plastic deformations of metals at high strain rates. Because they often precede rupture, their study attracted attenti…

math.AP2017

Conservation of energy for the Euler-Korteweg equations

Tomasz Dębiec, Piotr Gwiazda, Agnieszka Świerczewska-Gwiazda +1

In this article we study the principle of energy conservation for the Euler-Korteweg system. We formulate an Onsager-type sufficient regularity condition for weak solutions of the…

math.AP2016

Localization in inelastic rate dependent shearing deformations

Theodoros Katsaounis, Min-Gi Lee, Athanasios Tzavaras

Metals deformed at high strain rates can exhibit failure through formation of shear bands, a phenomenon often attributed to Hadamard instability and localization of the strain into…

math.AP2026

Equilibration versus Localization in a Diffusion-Relaxation System

Aseel AlNajjar, Hoyoun Kim, Athanasios Tzavaras

We consider a diffusion-relaxation system and investigate the conditions on parameters leading to equilibration versus localization. When the diffusion is dominant, solutions conve…

math.AP2011

Weak-strong uniqueness of dissipative measure-valued solutions for polyconvex elastodynamics

Sophia Demoulini, David Stuart, Athanasios Tzavaras

For the equations of elastodynamics with polyconvex stored energy, and some related simpler systems, we define a notion of dissipative measure-valued solution and show that such a…

math.AP2019

Localization in adiabatic shear flow via geometric theory of singular perturbations

Min-Gi Lee, Theodoros Katsaounis, Athanasios Tzavaras

We study localization occurring during high speed shear deformations of metals leading to the formation of shear bands. The localization instability results from the competition am…

math.AP2017

Relative entropy for hyperbolic-parabolic systems and application to the constitutive theory of thermoviscoelasticity

Cleopatra Christoforou, Athanasios Tzavaras

We extend the relative entropy identity to the class of hyperbolic-parabolic systems whose hyperbolic part is symmetrizable. The resulting identity, in the general theory, is usefu…