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We prove the existence of large-data global-in-time weak solutions to an evolutionary PDE system describing flows of incompressible \emph{heat-conducting} viscoelastic rate-type fluids with stress-diffusion, subject to a stick-slip boundary…

Analysis of PDEs · Mathematics 2020-07-14 Miroslav Bulíček , Josef Málek , Vít Průša , Endre Süli

This paper investigates a quasilinear parabolic system arising in thermoviscoelasticity of Kelvin-Voigt type with temperature-dependent viscosity and coupled terms. The system, given by \begin{equation*} \begin{cases}…

Analysis of PDEs · Mathematics 2026-03-11 Chuang Ma , Bin Guo

One of the main theoretical issues in developing a theory of anisotropic viscoelastic media at finite strains lies in the proper definition of the material symmetry group and its evolution with time. In this paper the matter is discussed…

Soft Condensed Matter · Physics 2021-02-03 Jacopo Ciambella , Paola Nardinocchi

We study a model for the deformation of a visco-elasto-plastic material that is nearly incompressible. It originates from geophysics, is given in the Eulerian description and combines a Kelvin-Voigt rheology in the spherical part with a…

Analysis of PDEs · Mathematics 2025-12-22 Thomas Eiter

We consider an elastic/viscoelastic transmission problem for the Bresse system with fully Dirichlet or Dirichlet-Neumann-Neumann boundary conditions. The physical model consists of three wave equations coupled in certain pattern. The system…

Analysis of PDEs · Mathematics 2022-02-23 Stéphane Gerbi , Chiraz Kassem , Ali Wehbe

An initial-boundary value problem for the multidimensional type III thermoelaticity for a nonsimple material with a center of symmetry is considered. In the linear case, the well-posedness with and without Kelvin-Voigt and/or frictional…

Analysis of PDEs · Mathematics 2016-05-09 Andrii Anikushyn , Michael Pokojovy

Motivated by the elastic-viscous-plastic (EVP) sea-ice model [E. C. Hunke and J. K. Dukowicz, J. Phys. Oceanogr., 27, 9 (1997), 1849--1867], which is used in large-scale numerical climate simulations, we proposed in [D. W. Boutros, X. Liu,…

Analysis of PDEs · Mathematics 2026-04-30 Daniel W. Boutros , Xin Liu , Marita Thomas , Edriss S. Titi

We prove that there exists a~large-data and global-in-time weak solution to a~system of partial differential equations describing an unsteady flow of an incompressible heat-conducting rate-type viscoelastic stress-diffusive fluid filling up…

Analysis of PDEs · Mathematics 2025-04-18 Michal Bathory , Miroslav Bulíček , Josef Málek

We propose a dynamical theory of low-temperature shear deformation in amorphous solids. Our analysis is based on molecular-dynamics simulations of a two-dimensional, two-component noncrystalline system. These numerical simulations reveal…

Statistical Mechanics · Physics 2009-10-30 M. L. Falk , J. S. Langer

A quasistatic nonlinear model for finite-strain poro-visco-elasticity is considered in the Lagrangian frame using Kelvin-Voigt rheology. The model consists of a mechanical equation which is coupled to a diffusion equation with a degenerate…

Analysis of PDEs · Mathematics 2024-08-28 Willem J. M. van Oosterhout

This study presents a comprehensive framework for constitutive modeling of a frame-invariant fractional-order approach to nonlocal thermoelasticity in solids. For this purpose, thermodynamic and mechanical balance laws are derived for…

Numerical Analysis · Mathematics 2021-02-11 Sai Sidhardh , Sansit Patnaik , Fabio Semperlotti

We propose thermodynamically consistent models for viscoelastic fluids with a stress diffusion term. In particular, we derive variants of compressible/incompressible Maxwell/Oldroyd-B models with a stress diffusion term in the evolution…

Fluid Dynamics · Physics 2018-03-14 Josef Málek , Vít Průša , Tomáš Skřivan , Endre Süli

A thermodynamically consistent model of non-classical coupled non-linear thermoelasticity capable of accounting for thermal wave propagation is proposed. The heat flux is assumed to consist of both additive energetic and dissipative…

Statistical Mechanics · Physics 2015-07-20 Mebratu F. Wakeni , B. D. Reddy , A. T. McBride

The equations of linearized viscoelastodynamics in Kelvin-Voigt rheology are rigorously derived from a nonlinear model that satisfies the time-dependent frame indifference in the sense of Antman. Besides showing the convergence of…

Analysis of PDEs · Mathematics 2026-03-04 Barbora Benešová , Malte Kampschulte , Martin Kružík

We introduce a one-dimensional stress-rate type nonlinear viscoelastic model for solids that obey the assumptions of the strain-limiting theory. Unlike the classical viscoelasticity theory, the critical hypothesis in the present…

Analysis of PDEs · Mathematics 2020-09-09 Husnu A. Erbay , Yasemin Sengul

We study a thermodynamically consistent model describing phenomena in a visco-plastic metal subjected to temperature changes. We complete the model with the mixed boundary condition on displacement and stress and Neumann-type condition for…

Analysis of PDEs · Mathematics 2014-08-13 Leszek Bartczak , Sebastian Owczarek

We consider a thermodynamically consistent model for thermoviscoplasticity. For the related PDE system, coupling the heat equation for the absolute temperature, the momentum balance with viscosity and inertia for the displacement variable,…

Analysis of PDEs · Mathematics 2018-03-20 Riccarda Rossi

This paper addresses a nonstationary flow of heat-conductive incompressible Newtonian fluid with temperature-dependent viscosity coupled with linear heat transfer with advection and a viscous heat source term, under Navier/Dirichlet…

Analysis of PDEs · Mathematics 2011-11-15 Luisa Consiglieri

In this work we study a quasi-static evolution of thermo-visco-elastic model with homogeneous thermal expansion. We assume that material is subject to two kinds of mechanical deformations: elastic and inelastic. Inelastic deformation is…

Analysis of PDEs · Mathematics 2016-11-17 Piotr Gwiazda , Filip Z. Klawe , Sebastian Owczarek

We establish the long-time existence of large-data weak solutions to a system of nonlinear partial differential equations. The system of interest governs the motion of non-Newtonian fluids described by a simplified viscoelastic rate-type…

Analysis of PDEs · Mathematics 2017-10-02 Miroslav Bulíček , Josef Málek , Vít Průša , Endre Süli