Related papers: Generalized solutions to linearized equations of T…

We propose a system of partial differential equations with a single constant delay $\tau > 0$ describing the behavior of a one-dimensional thermoelastic solid occupying a bounded interval of $\mathbb{R}^{1}$. For an initial-boundary value…

A mathematical model for an elastoplastic continuum subject to large strains is presented. The inelastic response is modeled within the frame of rate-dependent gradient plasticity for nonsimple materials. Heat diffuses through the continuum…

We consider the evolution of a small rigid body in an incompressible viscous fluid filling the whole space $\rline^3$. When the small rigid body shrinks to a "massless" point in the sense that its density is constant, we prove that the…

Thermodynamic relations are derived from first principles of mechanics for non-equilibrium processes. Since the key role herein is played by the law of increase of entropy, the latter is analyzed at first. It is shown that its derivation…

We formulate a quasistatic nonlinear model for nonsimple viscoelastic materials at a finite-strain setting in the Kelvin's-Voigt's rheology where the viscosity stress tensor complies with the principle of time-continuous frame-indifference.…

In order to provide a formally correct thermodynamical description of inhomogeneous fluids valid on all length scales down to the classical limit we postulate that all extensive quantities have locally extensive analogues. We derive local…

The letter considers non-isothermal fluid flows and revises simplifications of basic hydrodynamic equations for such flows arriving eventually to a generalization of the Oberbeck-Boussinesq approximation valid for arbitrary equation of…

The purpose of this review it to present a renewed perspective of the problem of self-gravitating elastic bodies under spherical symmetry. It is also a companion to the papers [Phys. Rev. D105, 044025 (2022)], [Phys. Rev. D106, L041502…

An ongoing problem in the study of a classical many-body system is the characterization of its equilibrium behaviour by theory or numerical simulation. For purely repulsive particles, locating the melting line in the pressure-temperature…

We develop a dynamical systems theory for the compressible Navier-Stokes equations based on global in time weak solutions. The following questions will be addressed: Global existence and critical values of the adiabatic constant;…

We consider the interaction of a compressible fluid with a flexible plate in two space dimensions. The fluid is described by the Navier--Stokes equations in a domain that is changing in accordance with the motion of the structure. The…

Experiments show that all the derivatives of the thermo-physical variables are nearly constant. The constant value of the derivatives indicates linear relationship between the variables. Neither the volume coefficient of thermal expansion…

We study an atomistic model that describes the microscopic formation of material voids inside elastically stressed solids under an additional curvature regularization at the discrete level. Using a discrete-to-continuum analysis, by means…

We introduce a simple model of the time evolution of a binary mixture of compressible fluids including the thermal effects. Despite its apparent simplicity, the model is thermodynamically consistent admitting an entropy balance equation. We…

Irreversible processes accomplished in a fixed time involve nonlinearly coupled flows of matter, energy, and information. Here, using entropy production as an example, we show how thermodynamic uncertainty relations and speed limits on…

We study a novel approach for the existence of solutions to an incompressible fluid-rigid body interaction problem in three dimensions. Our approach introduces an iteration based on a sequence of related problems posed on domains with…

We discuss several approaches to generalized solutions of problems describing the motion of inviscid fluids. We propose a new concept of dissipative solution to the compressible Euler system based on a careful analysis of possible…

A mathematical formulation of an estimation problem of a cavity inside a three-dimensional thermoelastic body using time domain data is considered. The governing equation of the problem is given by a system of equations in the linear theory…

This work is devoted to the consistent modeling of a three-phase mixture of a gas, a liquid and its vapor. Since the gas and the vapor are mis-cible, the mixture is subjected to a non-symmetric constraint on the volume. Adopting the Gibbs…

We define a nonlinear thermodynamical formalism which translates into dynamical system theory the statistical mechanics of generalized mean-field models, extending investigation of the quadratic case by Leplaideur and Watbled. Under…