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Size-dependence of energy transport and the effects of reduced dimensionality on transport coefficients are of key importance for understanding nonequilibrium properties of matter on the nanoscale. Here, we perform nonequilibrium and…

Statistical Mechanics · Physics 2021-05-26 Rongxiang Luo , Lisheng Huang , Stefano Lepri

We consider a system of stochastic partial differential equations modeling heat conduction in a non-linear medium. We show global existence of solutions for the system in Sobolev spaces of low regularity, including spaces with norm beneath…

Mathematical Physics · Physics 2007-05-23 Luc Rey-Bellet , Lawrence E. Thomas

In this paper, we prove the global existence of general small solutions to compressible viscoelastic system. We remove the "initial state" assumption ($\tilde \rho_0 \det F_0 =1$) and the "div-curl" structure assumption compared with…

Analysis of PDEs · Mathematics 2022-01-05 Yi Zhu

The extension of equilibrium thermodynamics to non-equilibrium systems is based on the assumption of "local equilibrium," followed by the assumption that an entropy-density function may be defined, and that this entropy-density would have…

Chemical Physics · Physics 2018-03-12 Arieh Ben-Naim

This paper is concerned with the analysis of the quasi-static thermo-poroelastic model. This model is nonlinear and includes thermal effects compared to the classical quasi-static poroelastic model (also known as Biot's model). It consists…

Analysis of PDEs · Mathematics 2018-07-05 Mats K. Brun , Elyes Ahmed , Florin A. Radu , Jan Martin Nordbotten

This paper deals with the study of a three-dimensional model of thermomechanical coupling for viscous solids exhibiting hysteresis effects. This model is written in accordance with the formalism of generalized standard materials and it is…

Analysis of PDEs · Mathematics 2011-11-11 Laetitia Paoli , Adrien Petrov

We demonstrate that the presence of entanglement in macroscopic bodies (e.g. solids) in thermodynamical equilibrium could be revealed by measuring heat-capacity. The idea is that if the system were in a separable state, then for certain…

Quantum Physics · Physics 2008-08-14 Marcin Wiesniak , Vlatko Vedral , Caslav Brukner

This article establishes the global existence of weak solutions to a model proposed by Rosensweig (Rosensweig, Ferrohydrodynamics (1985)) for the dynamics of ferrofluids. The system is expressed by the conservation of linear momentum, the…

Analysis of PDEs · Mathematics 2019-10-02 Ricardo H. Nochetto , Konstantina Trivisa , Franziska Weber

The backbone of nonequilibrium thermodynamics is the stability structure, where entropy is related to a Lyapunov function of thermodynamic equilibrium. Stability is the background of natural selection: unstable systems are temporary, and…

Physics and Society · Physics 2024-10-01 Peter Ván

We develop a global wellposedness theory for weak solutions to the 1D Euler-alignment system with measure-valued density, bounded velocity, and locally integrable communication protocol. A satisfactory understanding of the low-regularity…

Analysis of PDEs · Mathematics 2022-08-09 Trevor M. Leslie , Changhui Tan

We consider a thermodynamically consistent diffuse interface model describing two-phase flows of incompressible fluids in a non-isothermal setting. This model was recently introduced in a previous paper of ours, where we proved existence of…

Analysis of PDEs · Mathematics 2014-06-09 Michela Eleuteri , Elisabetta Rocca , Giulio Schimperna

We consider a quasistatic nonlinear model in thermoviscoelasticity at a finite-strain setting in the Kelvin-Voigt rheology where both the elastic and viscous stress tensors comply with the principle of frame indifference under rotations.…

Analysis of PDEs · Mathematics 2023-01-25 Rufat Badal , Manuel Friedrich , Martin Kružík

This paper analytically investigates the Darcy-Poisson-Nernst-Planck system. This system is a mathematical model for electrolyte solutions. In this paper, we consider electrolyte solutions, which consist of a neutral fluid and multiple…

Analysis of PDEs · Mathematics 2016-05-25 Matthias Herz , Peter Knabner

We study a model for a fluid showing viscoelastic and viscoplastic behavior, which describes the flow in terms of the fluid velocity and an internal stress. This stress tensor is transported via the Zaremba--Jaumann rate, and it is subject…

Analysis of PDEs · Mathematics 2023-12-22 Thomas Eiter , Katharina Hopf , Robert Lasarzik

This article studies the equations of adiabatic thermoelasticity endowed with an internal energy satisfying an appropriate quasiconvexity assumption which is associated to the symmetrisability condition for the system. A G{\aa}rding-type…

Analysis of PDEs · Mathematics 2021-10-01 Myrto Galanopoulou , Konstantinos Koumatos , Andreas Vikelis

This paper is concerned with a class of nonlinear reaction-hyperbolic systems as models for axonal transport in neuroscience. We show the global existence of entropy-satisfying BV-solutions to the initial-value problems by using…

Analysis of PDEs · Mathematics 2010-06-22 Hao Yan , Wen-An Yong

We develop a continuum theory for thermoelectric bodies following the framework of continuum mechanics and conforming to general principles of thermodynamics. For steady states, the governing equations for local fields are intrinsically…

Materials Science · Physics 2012-03-05 Liping Liu

We prove the existence and uniqueness of solutions for a family of nonlinear parabolic systems related to phase field models taking in account variations of temperature and the possibility of a general class of nonlinearities. The present…

Analysis of PDEs · Mathematics 2015-05-13 Anderson L. A. de Araujo , José L. Boldrini , Bianca M. R. Calsavara

Here we investigate global strong solutions for a class of partially dissipative hyperbolic systems in the framework of critical homogeneous Besov spaces. Our primary goal is to extend the analysis of our previous paper [10] to a functional…

Analysis of PDEs · Mathematics 2022-01-19 Timothée Crin-Barat , Raphaël Danchin

Understanding heat transport in low-dimensional and nano-architectured materials remains a central challenge in nonequilibrium statistical physics due to persistent deviations from Fourier's law. These deviations are driven by…

Mesoscale and Nanoscale Physics · Physics 2026-05-15 R. A. C. Correa , K. N. M. Sharma , P. Lolur , J. van Velzen