Boundary behavior of the solution to the linear Korteweg-De Vries equation on the half line

In this paper, we consider the solution to the linear Korteweg-De Vries (KdV) equation, both homogeneous and forced, on the quadrant $\{x\in {\mathbb{R}}^{+},t\in {\mathbb{R}}^{+}\}$ via the unified transform method of Fokas and we provide a complete rigorous study of the integrals of the formula provided by the method, especially focusing on the explicit verification of the considered initial-boundary-value problems (IBVPs), with generic data, as well as on the uniform convergence of all its derivatives, as $(x,t)$ approaches the boundary of the quadrant, and their rapid decay as $x\to \infty$.     

On the evolution of particle size average and size distribution in suspension polymerization processes

The dispersion of methyl methacrylate (MMA) and its suspension polymerization were used as models to elaborate the evolution of particle size average and size distribution in the course of suspension polymerization. The underlying mechanisms for the occurrence of the dynamic and static steady states in the population of drops were defined and their effects on the evolution of drop/particle size average and size distributions were examined. The characteristic intervals of suspension polymerizations (transition, steady-state, growth, and identification) were elaborated. The formation of satellite droplets and their evolution in the course of polymerization were also discussed.     

Laser cooling of solids [Laser Photon. Rev. 3, No. 1–2, 67–84 (2009)]

Fig. 7b and Figs. 14a and b in the paper published in Laser Photon. Rev. 3 , 67–84 have not been referenced completely. Please find the correct figure captions here.     

具有加权非局部边界条件的多孔介质方程组的临界指标问题

本文研究了具有非局部边界条件和非线性内部源的多孔介质抛物型方程组问题。利用比较原理,获得了权函数和系数对整体解和爆破解的影响,并得到了解的爆破临界指标,推广了先前的研究结果。