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We show that small perturbations of the spatially homogeneous equilibrium of a thermally driven compressible viscous fluid are globally stable. Specifically, any weak solution of the evolutionary Navier--Stokes--Fourier system driven by…
In this paper, we present the analysis of stability for a piezoelectric beam subject to a thermal law (Coleman-Gurtin or Gurtin-Pipkin thermal law) adding some viscous damping mechanism to the electric field in $x-$direction and…
System of partial differential equations with a convolution terms and non-local nonlinearity describing oscillations of plate due to Berger approach and with accounting for thermal regime in terms of Coleman-Gurtin and Gurtin-Pipkin law and…
We study a system of two coupled nonlinear parabolic equations. It constitutes a variant of the Keller-Segel model for chemotaxis, i.e. it models the behaviour of a population of bacteria that interact by means of a signalling substance. We…
This article is concerned with the energy decay of an infinite memory wave equation with a logarithmic nonlinear term and a frictional damping term. The problem is formulated in a bounded domain in $\mathbb R^d$ ($d\ge3$) with a smooth…
The purpose of this work is to investigate the exponential stability of a second order coupled wave equations by laplacian with one locally internal viscous damping. Firstly, using a unique continuation theorem combined with a Carleman…
Understanding under what conditions it is possible to construct equivalent ensembles is key to advancing our ability to connect microscopic and macroscopic properties of non-equilibrium statistical mechanics. In the case of fluid dynamical…
We use optical trapping to continuously bend an isolated microtubule while simultaneously measuring the applied force and the resulting filament strain, thus allowing us to determine its elastic properties over a wide range of applied…
We consider a non-Newtonian incompressible heat conducting fluid with prescribed nonuniform temperature on the boundary and with the no-slip boundary conditions for the velocity. We assume no external body forces. For the power-law like…
In this paper, we develop a multiphysics finite element method for solving the quasi-static thermo-poroelasticity model with nonlinear permeability. The model involves multiple physical processes such as deformation, pressure, diffusion and…
The purpose of this work is to provide an explicit construction of a strong Feller semigroup on the space of probability measures over the real line that additionally maps bounded measurable functions into Lipschitz continuous functions,…
We consider vibrations of an inhomogeneous flexible structure modeled by a $1$D viscoelastic equation with Kelvin-Voigt, coupled with an expected dissipative effect : heat conduction governed by Cattaneo's law (second sound). We establish…
Nonlinear entropy stability analysis is used to derive entropy stable no-slip wall boundary conditions for the Eulerian model proposed by Sv\"{a}rd (Physica A: Statistical Mechanics and its Applications, 2018). and its spatial…
Moist thermodynamics is a fundamental driver of atmospheric dynamics across all scales, making accurate modeling of these processes essential for reliable weather forecasts and climate change projections. However, atmospheric models often…
The dynamics and thermodynamics of melting in two-dimensional Coulomb clusters is revisited using molecular dynamics and Monte Carlo simulations. Several parameters are considered, including the Lindemann index, the largest Lyapunov…
Using quantum gas microscopy we study the late-time effective hydrodynamics of an isolated cold-atom Fermi-Hubbard system subject to an external linear potential (a "tilt"). The tilt is along one of the principal directions of the…
The inviscid, partial differential equations of hydrodynamics when projected via a Galerkin-truncation on a finite-dimensional subspace spanning wavenumbers $-{\bf K}_{\rm G} \le {\bf k} \le {\bf K}_{\rm G}$, and hence retaining a finite…
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…
In this work, the multiplier method is extended to obtain a general lower bound of the exponential decay rate in terms of the physical parameters for port-Hamiltonian systems in one space dimension with boundary dissipation. The physical…
We study the exponential stability of constant steady state of isentropic compressible Euler equation with damping on $\mathbb T^n$. The local existence of solutions is based on semigroup theory and some commutator estimates. We propose a…