Related papers: Entropy Admissibility of the Limit Solution for a …
We obtain new transport-entropy inequalities and, as a by-product, new deviation estimates for the laws of two kinds of discrete stochastic approximation schemes. The first one refers to the law of an Euler like discretization scheme of a…
This work studies a macroscopic traffic flow model driven by a system of nonlinear hyperbolic partial differential equations. Using Lie symmetry analysis, we determine the infinitesimal generators and construct an optimal system of…
We study nontrivial entropy invariants in the class of parabolic flows on homogeneous spaces, quasi-unipotent flows. We show that topological complexity (ie, slow entropy) can be computed directly from the Jordan block structure of the…
This study derived the vertical distribution of streamwise velocity in wide open channels by maximizing Tsallis entropy, in accordance with the maximum entropy principle, subject to the total probability rule and the conservation of mass,…
We consider the sharp interface limit of a convective Allen-Cahn equation, which can be part of a Navier-Stokes/Allen-Cahn system, for different scalings of the mobility $m_\varepsilon=m_0\varepsilon^\theta$ as $\varepsilon\to 0$. In the…
We study a degenerate parabolic-hyperbolic equation with zero flux boundary condition. The aim of this paper is to prove convergence of numerical approximate solutions towards the unique entropy solution. We propose an implicit finite…
This paper is devoted to a nonlocal reaction-diffusion-advection model that describes the spatial dynamics of freshwater organisms in a river with a directional motion. Our goal is to investigate how the advection rate affects the dynamic…
We prove the convergence of the vanishing viscosity limit of the one-dimensional, isentropic, compressible Navier-Stokes equations to the isentropic Euler equations in the case of a general pressure law. Our strategy relies on the…
We consider a modified Nagel-Schreckenberg (NS) model in which drivers do not decelerate if their speed is smaller than the headway (number of empty sites to the car ahead). (In the original NS model, such a reduction in speed occurs with…
We introduce an energy dissipation model for traffic flow based on the optimal velocity model (OV model). In this model, vehicles are defined as moving under the rule of the OV model, and energy dissipation rate is defined as the product of…
We consider the asymptotic behavior of compressible isentropic flow when the initial mass is finite, which is modeled by the compressible Euler equation with frictional damping. It is shown in \cite{HUA} (resp.\cite{GEN}) that any…
Under a precise genuine nonlinearity assumption we establish the decay of entropy solutions of a multidimensional scalar conservation law with merely continuous flux.
We introduce a novel Entropy-driven Monte Carlo (EdMC) strategy to efficiently sample solutions of random Constraint Satisfaction Problems (CSPs). First, we extend a recent result that, using a large-deviation analysis, shows that the…
We study vehicular traffic on a road with multiple lanes and dense, unidirectional traffic following the traditional Lighthill-Whitham-Richards model where the velocity in each lane depends only on the density in the same lane. The model…
We consider solutions to the full (non-isentropic) two-dimensional Euler equations that are constant in time and along rays emanating from the origin. We prove that for a polytropic equation of state, entropy admissible solutions in…
In this paper we analyze the long-time behavior of solutions to conservation laws with nonlinear diffusion terms of different types: saturating dissipation (monotone and non monotone) and singular nonlinear diffusions are considered. In…
The aim of this work is to analyze the entropy, entropy flux and entropy supply rate of granular fluids within the frameworks of the Boltzmann equation and continuum thermodynamics. It is shown that the entropy inequality for a granular gas…
We study the quasilinear Maxwell system with a strictly positive, state dependent boundary conductivity. For small data we show that the solution exists for all times and decays exponentially to $0$. As in related literature we assume a…
We build a finite volume scheme for the scalar conservation law $\partial_t u + \partial_x (H(x, u)) = 0$ with bounded initial condition for a wide class of flux function $H$, convex with respect to the second variable. The main idea for…
Recently, A. Vasseur and C. Yu have proved the existence of global entropy-weak solutions to the compressible Navier-Stokes equations with viscosities $\nu(\varrho)=\mu\varrho$ and $\lambda(\varrho)=0$ and a pressure law under the form…