Quasi-neutral limit for the full Euler–Poisson system in one-dimensional space

In this paper, we consider the quasi-neutral limit of the full Euler–Poisson system in one-dimensional space when the Debye length tends to zero. Due to the observation that the full Euler–Poisson system is Friedrich symmetrizable, we can obtain uniform estimates by applying the pseudo-differential energy estimates. It is shown that for well-prepared initial data the strong solution of the full Euler–Poisson system converges strongly to the compressible Euler equations in small time interval.     

Convergence of numerical solutions for variable delay differential equations driven by Poisson random jump measure

We study the following stochastic differential delay equations driven by Poisson random jump measure

     

有限初始能量的相对论欧拉方程组光滑解的爆破

在初始资料的某些限制下证明有限初始能量的相对论欧拉方程组柯西问题光滑解的爆破.该文的爆破条件不需要初始资料具有紧支集,部分补充了Pan和Smoller的经典爆破结果(2006).     

Global and blow‐up solutions for non‐linear degenerate parabolic systems

In this paper the degenerate parabolic system u_t=u(u_xx+av). vt=v(v_xx+bu) with Dirichlet boundary condition is studied. For , the global existence and the asymptotic behaviour (α₁=α₂) of solution are analysed. For , the blow‐up time, blow‐up rate and blow‐up set of blow‐up solution are estimated and the asymptotic behaviour of solution near the blow‐up time is discussed by using the ‘energy’ method. Copyright © 2003 John Wiley & Sons, Ltd.     

2-一致光滑空间中严格伪压缩映像的弱收敛定理

讨论了严格伪压缩映像的不动点问题.在2-一致光滑一致凸的Banach空间中,通过Mann迭代方法得到严格伪压缩映像的不动点的弱收敛结果.这个结果推广了目前的已知结果.     

Existence and Uniqueness of the Global Smooth Solution to the Periodic Boundary Value Problem of Fractional Nonlinear Schrödinger System

In this paper, we study a class of coupled fractional nonlinear Schrödinger system with periodic boundary condition. Using Galerkin method, the existence of global smooth solution is obtained. We also prove the uniqueness of the solution.     

Global smooth solution to a coupled Schrödinger system in atomic Bose-Einstein condensates with two-dimensional spaces

We obtain the global smooth solution of a nonlinear Schrödinger equations in atomic Bose-Einstein condensates with two-dimensional spaces. By using the Galerkin method and a priori estimates, we establish the global existence and uniqueness of the smooth solution.     

On the Nonexistence of Global Weak Solutions to the Navier–Stokes–Poisson Equations in ℝ N

In this paper we prove nonexistence of stationary weak solutions to the Euler–Poisson equations and the Navier–Stokes–Poisson equations in ? ^N , N ≥ 2, under suitable assumptions of integrability for the density, velocity and the potential of the force field. For the time dependent Euler–Poisson equations we prove nonexistence result assuming additionally temporal asymptotic behavior near infinity of the second moment of density. For a class of time dependent Navier–Stokes–Poisson equations in ? ^N this asymptotic behavior of the density can be proved if we assume the standard energy inequality, and therefore the nonexistence of global weak solution follows from more plausible assumption in this case.     

Local Existence of the Shock Front Solution to the Axi-symmetrical Piston Problem in Compressible Flow

In this paper, we study a kind of 2-dimensional axi-symmetrical piston problem in compressible flow. The corresponding mathematical model is the well-known Euler system. With the Newton iteration procedure and energy estimate, we give the local existence of the shock front solution to this problem.     

Local Existence of the Shock Front Solution to the Axi-symmetrical Piston Problem in Compressible Flow

In this paper,we study a kind of 2-dimensional axi-symmetrical piston problem in com-pressible flow.The corresponding mathematical model is the well-known Euler system.With theNewton iteration procedure and energy estimate,we give the local existence of the shock front solutionto this problem.     

Banach空间中Lipschitz伪压缩映射的近似不动点序列及其收敛定理

研究了Lipschitz伪压缩映射的黏滞迭代方法.设E为一致光滑Bannach空间,K为E的闭凸子集,TK→K为Lipschitz伪压缩映射且其不动点集F(T)非空,f为K上的压缩映射且t∈(0,1).若黏滞迭代路径{xt},xt=(1-t)f(xt) tTxt且对任意初始向量x1∈K,迭代序列{xn}定义为xn 1=λnθnf(xn) [1-λn(1 θn)]xn λnTxn,则当t→1-和n→∞时,{xt}和{xn}都强收敛于T的不动点,同时该不动点还是一类变分不等式的解.