In this paper, we are concerned with the initial boundary valueproblem on two-fluid Navier-Stokes-Poisson system in thehalf-line $R_+$. We establish global-in-time asymptoticstability of rarefaction wave and layer both forthe outflow problem under smallness assumption initialperturbation, where strength is notnecessarily small while isadditionally supposed to be small. Here, large data withdensities far from vacuum also allowed case thenon-degenerate layer. The results show that...

This paper considers individual-based crowd dynamics with social interaction. The investigation entails interpreting pedestrians as active particles. Besides the mechanical variables, typically position and velocity, an activity variable is introduced into modeling framework, which represents evolving psychological states of pedestrians. can interact that variables thus affecting interaction rules. approach useful for describing heterogeneous behavioral features in crowds, especially, states.

In the present work, we consider well-posedness and asymptotics of grazing collisions limit spatially inhomogeneous Boltzmann equation with Coulomb interaction. Under screening hypothesis on cross-section $B^\epsilon(z,\sigma)$ collision operator, that is, $ B^\epsilon(z, \sigma)=|\log \epsilon|^{-1}|z|^{-3}\theta^{-3}(\sin\theta)^{-1}{1}_{\{\theta\ge \epsilon\}}$, where $\cos\theta= \frac{z}{|z|}\cdot\sigma$, prove there exists a common lifespan $T$ such for any $\epsilon$, admits unique...

We study the dissipation of solutions for isentropic Navier–Stokes equations in even space-dimensions. Based on global existence and analysis Green function associated with linearized system, pointwise estimates solution are established. It is observed here that dimensions time-asymptotic behavior follows from weak Huygen's principle.

In this paper, we study a kinetic modeling of opinion formation on social networks in which the distribution function depends both and connectivity agents. The exchange process is governed by Sznajd-type model with three opinions, [Formula: see text], 0, network represented statistically denoting number contacts given individual. It commonly accepted that, networks, agents higher connectivity, i.e. larger followers, more convincing than that lower followers. By approach, derived asymptotic...

Many physical models have boundaries. For the Boltzmann equation, study on boundary layer in region of width order Kundsen number along is important both mathematics and physics. In this paper, we consider nonlinear stability solutions to equation for hard potentials with angular cut-off. The condition imposed incoming particles Dirichlet type solution tends a global Maxwellian far field. existence solutions, it proved by Chen et al. [Anal. Appl. 2, 337–363 (2004)] introducing weight...

The kinetic boundary layer for gas mixtures is described by a half space value problem the two-species steady Boltzmann equation with an incoming distribution. We consider it around drifting normalized bi-Maxwellian and prove that well-posed when velocity u exceeds sound speed , but one (respectively five, six) additional condition must be imposed ).

When the Boltzmann equation is used to study a physical problem with boundary, there usually exists layer of width in order Knudsen number along boundary. There have been extensive studies on existence and stability boundary layers different settings. Based previous work, this paper, we consider solutions for cutoff soft potentials when its parameter γ satisfying −2<γ⩽0. The condition imposed incoming particles Dirichlet type, solution assumed approach global Maxwellian at far field....

In this paper, we derive an a prioriL 2 -stability estimate for classical solutions to the relativistic Boltzmann equation, when initial datum is small perturbation of global Maxwellian. For stability estimate, use dissipative property linearized collision operator and Strichartz type solutions. As direct application our estimates, establish that in Glassey–Strauss Hsiao–Yu's frameworks satisfy uniform L estimate.

In this paper, we study the nonlinear stability and pointwise structure around a constant equilibrium for radiation hydrodynamic model in 1‐dimension, which behavior of fluid is described by full Euler equation with certain effect. It well‐known that classical solutions 1‐D may blow up finite time general initial data. The global existence solution paper means effect stabilizes system prevents formation singularity when data small. To precise model, also treat estimates original problem...