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In this paper, we are concerned with the one-species VlasovPoissonBoltzmann system with a nonconstant background density in full space. There exists a stationary solution when the background density is a small perturbation of a positive constant state. We prove the nonlinear stability of solutions to the Cauchy problem near the stationary state in some Sobolev space without any time derivatives. This result is nontrivial even when the background density is a constant state. In the proof, the macroscopic balance laws are essentially used to deal with the a priori estimates on both the microscopic and macroscopic parts of the solution. Moreover, some interactive energy functionals are introduced to overcome difficulty stemming from the absence of time derivatives in the energy functional.

This paper presents a general methodology to design macroscopic fluid models that take into account localized kinetic upscaling effects. The fluid models are solved in the whole domain together with a localized kinetic upscaling that corrects the fluid model wherever it is necessary. This upscaling is obtained by solving a kinetic equation on the nonequilibrium part of the distri-bution function. This equation is solved only locally and is related to the fluid equation through a downscaling effect. The method does not need to find an interface condition as do usual domain decomposition methods to match fluid and kinetic representations. We show our approach applies to problems that have a hydrodynamic time scale as well as to problems with diffusion time scale. Simple numerical schemes are proposed to discretize our models, and several numerical examples are used to validate the method.

In this work, we study the stability of the expanding configurations for radiation gaseous stars. Such expanding configurations exist for the isentropic model and the thermodynamic model. In particular, we focus on the effect of the monatomic gas viscosity tensor on the expanding configurations. With respect to small perturbation, it is shown the self-similarly expanding homogeneous solutions of the isentropic model is unstable, while the linearly expanding homogeneous solutions of the isentropic model and the thermodynamic model are stable. This is an extensive study of the result in arXiv: 1605.08083 by Hadzic and Jang.

A computational method, based on ₁-minimization, is proposed for the problem of link flow correction, when the available traffic flow data on many links in a road network are inconsistent with respect to the flow conservation law. Without extra information, the problem is generally ill-posed when a large portion of the link sensors are unhealthy. It is possible, however, to correct the corrupted link flows accurately with the proposed method under a recoverability condition if there are only a few bad sensors which are located at certain links. We analytically identify the links that are robust to miscounts and relate them to the geometric structure of the traffic network by introducing the recoverability concept and an algorithm for computing it. The recoverability condition for corrupted links is simply the associated recoverability being greater than 1. In a more realistic setting, besides the unhealthy link sensors, small