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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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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.…
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…
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…
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…
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…
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…
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…
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…
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…