Related papers: Energy dissipation admissibility condition for con…
This paper concerns with the compressible two-fluid model with algebraic pressure closure. We prove a conditional weak-strong uniqueness principle, meaning that a finite energy weak solution, with bounded densities, coincides with the…
Absorption of electromagnetic energy by a dissipative material is one of the most fundamental electromagnetic processes that underlies a plethora of applied problems, including sensing and molecular detection, radar detection, wireless…
The numerical integration of phase-field equations is a delicate task which needs to recover at the discrete level intrinsic properties of the solution such as energy dissipation and maximum principle. Although the theory of energy…
We study the diffusive limit approximation for a nonlinear radiative heat transfer system that arises in the modeling of glass cooling, greenhouse effects and in astrophysics. The model is considered with the reflective radiative boundary…
We consider conservation laws with nonlocal velocity and show for nonlocal weights of exponential type that the unique solutions converge in a weak or strong sense (dependent on the regularity of the velocity) to the entropy solution of the…
This study proposes a novel spatial discretization procedure for the compressible Euler equations which guarantees entropy conservation at a discrete level when an arbitrary equation of state is assumed. The proposed method, based on a…
We investigate the relation between several generalized solution concepts for nonlinear PDE systems from fluid dynamics. More precisely, we study measure-valued solutions, dissipative weak solutions, and energy-variational solutions. For…
We introduce an energy-based model, which seems especially suited for constrained systems. The proposed model provides an alternative to the popular port-Hamiltonian framework and exhibits similar properties such as energy dissipation as…
Energy conservations are studied for inhomogeneous incompressible and compressible Euler equations with general pressure law in a torus or a bounded domain. We provide sufficient conditions for a weak solution to conserve the energy. By…
A weak formulation for the so-called "semilinear strongly damped wave equation with constraint" is introduced and a corresponding notion of solution is defined. The main idea in this approach consists in the use of duality techniques in…
We show how to adapt the approach introduced for viscous damping in [1] to derive the approximate amplitude decay in the case of damping by a force of constant magnitude (sliding friction) and in the case of damping by a force proportional…
The paper deals with the problem of the energy conservation for the weak solutions to the compressible Primitive Equations (CPE) system with degenerate viscosity. The sufficient conditions on the regularity of weak solutions for the energy…
Vibrating systems can respond to an infinite number of initial conditions and the overall dynamics of the system can be strongly affected by them. Therefore, it is of practical importance to have methods by which we can determine the…
In a recent paper, PNAS, 118, e1921529118 (2021), it was argued that while the standard definition of conservation laws in quantum mechanics, which is of a statistical character, is perfectly valid, it misses essential features of nature…
In this paper we provide a rigorous derivation of the inelastic linear Boltzmann equation, in the Boltzmann-Grad limit, from a dissipative, random, Lorentz gas in arbitrary dimensions d $\geq$ 2. Specifically, we consider a microscopic…
We consider the numerical approximation of compressible flow in a pipe network. Appropriate coupling conditions are formulated that allow us to derive a variational characterization of solutions and to prove global balance laws for the…
In the present contribution, we investigate first-order nonlinear systems of partial differential equations which are constituted of two parts: a system of conservation laws and non-conservative first order terms. Whereas the theory of…
Single file systems are simplified models to study effectively one-dimensional physical systems. Here we compute analytically the complete first exit time statistics for an ideal overdamped single file with absorbing boundary conditions.…
Inspired by Jacobson's thermodynamic approach[gr-qc/9504004], Cai et al [hep-th/0501055,hep-th/0609128] have shown the emergence of Friedmann equations from the first law of thermodynamics. We extend Akbar--Cai derivation [hep-th/0609128]…
This article is concerned with the dynamics of a mixture of gases. Under the assumption that all the gases are isothermal and inviscid, we show that the governing equations have an elegant conservation-dissipation structure. With the help…