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.     

Large Time Behavior of a Weak Solution for Non-Newtonian Flow

This paper concerns large time behavior of a regular weak solution for non-Newtonian flow equations. It is shown that the decay of the solution is of exponential type when the force term is equal to zero and the domain is bounded. Moreover, the ratio of the enstrophy over the energy has a limit as time tends to infinity, which is an eigenvalue of the Stokes operator.     

Inverse Piston Problem for the System of One-Dimensional Isentropic Flow

In this paper, the authors consider the inverse piston problem for the system of one-dimensional isentropic flow and obtain that, under suitable conditions, the piston velocity can be uniquely determined by the initial state of the gas on the right side of the piston and the position of the forward shock.     

Existence of the Global Smooth Solution to the Period Boundary Value Problem of Fractional Nonlinear Schrodinger Equation

It is well known that Feynman and Hibbs[1] used path integrals over Brownian paths to derive the standard(nonfractional) Schrodinger equation. Recently, Laskin[5, 6] showed that the path integral over the Lévy-like quantum mechanical paths allows to develop the generalization of the quantum mechanics. Namely, if the path integral over Brownian trajectories leads to the well known Schrodinger equation, then the path integral over Lévy trajectories leads to the fractional Schrodinger equation. Laskin[7] showed the Hermiticity of the fractional Hamilton operator and established the parity conservation law. Xiaoyi Guo and Mingyu Xu[4] studied some physical applications of the fractional Schrodinger equation.     

Existence of Weak Solutions of Two-dimensional Euler Equations with Initial Vorticity in Lorentz Space L （2,1） （ R^2）

Some estimates on 2-D Euler equations are given when initial vorticity ω0 belongs to a Lorentz space L(2, 1). Then based on these estimates, it is proved that there exist global weak solutions of two dimensional Euler equations when ωo ∈ L(2, 1).     

The Existence of Weak Solutions to the 2D Euler Equations with Initial Vorticity in BMO

We shall prove that there exists a weak solution to the 2D Euler equations with initial vorticity in BMO and initial velocity in L^∞.     

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.     

Solutions to the Definite Solution Problem of Differential Equations in Space W_2~l

In this PaPer,we diseuss the definite solution Problem of differential equations in Hilbert funetion sPaeeW_2~l.Aeeording to different definite solutionProblems,we ehoose the eorresPonding     

Existence and Nonuniqueness of Weak Solutions of the Initial-Boundary Value Problem for ut=u^σ div（｜△↓u｜^（p-2）△↓u）

In this paper, we study the existence and nonuniqueness of weak solutions of the initial and boundary value problem for ut =u^σ div(|△↓u|^(p-2)△↓u) with σ≥1. Localization property of weak solutions is also discussed.     

一维活塞问题激波解的整体存在性

本文用改进的Glimm格式的方法,研究一维活塞问题当活塞的运动速度是一个常数的扰动时含有激波的弱解的存在性.对波的相互作用以及扰动波在主激波和活塞上的反射作出了精确的估计,在对主激波的强度不加限制的情况下证明了激波解的整体存在性.     

二维等熵可压欧拉方程古典解的存在性(英文)

研究二维等熵可压缩欧拉方程的古典解存在性.利用迭代技巧,得到解的局部存在性及唯一性,并且还证明了解在有限时间内爆破,即可压缩欧拉方程不存在全局古典解.     

一维可压Navier—Stokes方程初边值问题局部解的存在性

我们证明了半空间中一维可压Navier—Stokes方程初边值问题局部解的存在性,证明主要是利用了能量方法．     

Lidstone边值问题正解的单调迭代

考察了Lidstone边值问题正解的单调迭代. 这个迭代程序是从常值函数开始并且是可行的.     

Global Stability of Multi-wave Configurations for the Compressible Non-isentropic Euler System

This paper is contributed to the structural stability of multi-wave configurations to Cauchy problem for the compressible non-isentropic Euler system with adiabatic exponent γ ∈ (1, 3]. Given some small BV perturbations of the initial state, the author employs a modified wave front tracking method, constructs a new Glimm functional, and proves its monotone decreasing based on the possible local wave interaction estimates, then establishes the global stability of the multi-wave configurations, onsisting of a strong 1-shock wave, a strong 2-contact discontinuity, and a strong 3-shock wave, without restrictions on their strengths.     

关于线性互补问题解的存在性

讨论线性互补问题解的存在性。证明关于解的唯一性定理。用反例表明:对于线性互补问题解的存在性,"M是半正定矩阵"既不是充分条件,也不是必要条件。     

二维可压缩Euler方程组C^1解整体存在的必要条件

对于具有某类初值条件的二维可压缩流体Euler方程组，给出了其C1解整体存在的必要条件，从而对[1]、[2]中的“未解决问题”提供了有意义的说明．     

2n阶Lidstone边值问题正解的逐次迭代

研究了2n阶Lidstone边值问题正解的逐次迭代,其中非线性项依赖于所有偶数阶导数.通过考察非线性项在某些有国介集合上的“高度”并利用单调迭代方法构造了一个逐次迭代程序.这个迭代程序从一个多项式开始并且是可行的.使用这个结论获得了m个正解的迭代方法,其中m是一个任意的自然数.