Global existence and time decay of the non-cutoff Boltzmann equation with hard potential

This paper is concerned with the Cauchy problem on the Boltzmann equation without angular cutoff assumption for hard potential in the whole space. When the initial data is a small perturbation of a global Maxwellian, the global existence of solution to this problem is proved in unweighted Sobolev spaces $H^N\left({\mathbb{R}}_{x,v}^6\right)$ with $N\ge 2$. But if we want to obtain the optimal temporal decay estimates, we need to add the velocity weight function, in this case the global existence and the optimal temporal decay estimate of the Boltzmann equation are all established. Meanwhile, we further gain a more accurate energy estimate, which can guarantee the validity of the assumption in Chen et al. (0000).     

Full cross-diffusion limit in the stationary Shigesada-Kawasaki-Teramoto model

This paper studies the asymptotic behavior of coexistence steady-states of the Shigesada-Kawasaki-Teramoto model as both cross-diffusion coefficients tend to infinity at the same rate. In the case when either one of two cross-diffusion coefficients tends to infinity, Lou and Ni [18] derived a couple of limiting systems, which characterize the asymptotic behavior of coexistence steady-states. Recently, a formal observation by Kan-on [10] implied the existence of a limiting system including the nonstationary problem as both cross-diffusion coefficients tend to infinity at the same rate. This paper gives a rigorous proof of his observation as far as the stationary problem. As a key ingredient of the proof, we establish a uniform $L^{\infty }$ estimate for all steady-states. Thanks to this a priori estimate, we show that the asymptotic profile of coexistence steady-states can be characterized by a solution of the limiting system.     

Enhanced dielectric and nonohmic properties of SrTiO3-modified CaCu3Ti4O12 ceramics

Dielectric and nonohmic properties of CaCu₃Ti₄O₁₂ (CCTO) ceramics can be modified by addition of SrTiO₃ (STO) in different molar proportions which were fabricated by a modified sol-gel method. XRD results indicated that all modified ceramics showed mixed phase consisting of both CCTO and STO. SEM images and grain size distribution probability also presented the change of microstructure with the addition of STO. The dielectric loss of the CCTO/0.4STO ceramics sintered at 1000 °C can be lower than 0.02 in a wide frequency (1 kHz–10 kHz), especially at 1 kHz, the dielectric loss of this sample is as low as 0.012. Furthermore, excellent nonlinear I–V electrical characteristic (high breakdown voltage to 54.15 kV/cm for CCTO/0.4STO sintered at 1000 °C) was observed as well. All the results indicated that the addition of STO does improve the dielectric properties and nonohmic characteristics of CCTO ceramics dramatically.