一类具非线性二阶导数项的Schr dinger方程整体解存在的最佳条件

本文讨论一类具非线性二阶导数项的Schr(?)dinger方程,它在物理上描述了上混合振荡传播．根据基态的变分特征,运用势井方法和凹方法,我们获得了其初值问题整体解存在的一个最佳条件,另外还证明了当初值多小时,初值问题的整体解存在．     

具耗散项p-方程组的整体光滑解

该文考虑具耗散项的p-方程组初值问题的整体光滑解．我们在假设初值的振幅为任意给定，而其导数适当小时，得到了初值问题整体光滑解的存在性．     

一类具非线性二阶导数项的Schrödinger方程整体解存在的最佳条件

本文讨论一类具非线性二阶导数项的schr(o)dinger方程,它在物理上描述了上混合振荡传播.根据基态的变分特征,运用势井方法和凹方法,我们获得了其初值问题整体解存在的一个最佳条件,另外还证明了当初值多小时,初值问题的整体解存在.     

一类具非线性二阶导数项的Schr(o)dinger方程整体解存在的最佳条件

本文讨论一类具非线性二阶导数项的schr(o)dinger方程,它在物理上描述了上混合振荡传播.根据基态的变分特征,运用势井方法和凹方法,我们获得了其初值问题整体解存在的一个最佳条件,另外还证明了当初值多小时,初值问题的整体解存在.     

二维Newton-Boussinesq方程周期初值问题经典解的整体存在性

研究一类二维Newton-Boussinesq方程的周期初值问题,将方程转化为积分方程,用不动点原理得到解的局部存在性,用能量估计的方法证明经典解的整体存在性．     

一类非线性积－微分方程极值解的存在性定理

本文讨论非线性积－微分方程初值问题的极值解的存在性．其中“利用单调迭代法和上、下解方法，得到了最小解和最大解的存在性定理．     

浅水波方程的初边值问题

本文用Kato关于拟线性演化方程的初值问题的存在性定理证明了浅水波方程在半无界直线上初值问题局部解的存在性。用解的先估计证明了整体解的存在性或解的Blow-up性质，并给出了解关于x的渐近估计。     

无限区间上的 Banach 空间积-微分方程的初值问题的上下解方法

建立了无限区间上的积一微分方程的比较定理,用上下解方法证明了无限区间上的Banach空间积-微分方程的初值问题的解的存在性．     

二阶非线性积-微分方程的初值问题的上下解方法

建立了无限区间上二阶积－微分方程的比较定理,用上下解方法证明了无限区间上的Ｂａ－ｎａｃｈ空间二阶非线性积－微分方程的初值问题的解的存在性．     

具耗散项的绝热气动力学方程组的整体光滑解

考虑拉格朗日坐标下具耗散项的绝热气动力学方程组的初值问题，分别证明了其整体光滑解的存在性与非存在性．     

一类Boussinesq型方程整体解的存在性和唯一性

证明一类6阶Boussinesq型方程Cauchy问题整体广义解和整体古典解的存在性和唯一性,给出解在有限时刻发生爆破的充分条件.     

Coexistence and Asymptotic Periodicity in a Competition Model of Plankton Allelopathy

In this paper, the two species Lotka-Volterra competition model of plankton allelopathy from aquatic ecology is discussed. The authors study the existence of solutions to a strongly coupled elliptic system with homogeneous Dirichlet boundary conditions and consider the existence, stability and global attractivity of time-periodic solutions for a coupled parabolic equations in a bounded domain. Their results show that this model possesses at least one coexistence state if cross-diffusions and self-diffusions are weak. The existence of the positive T-periodic solutions and the global stability as well as the global attractivity for the parabolic system are also given.     

Kuramoto-Sivashinsky方程解的定性分析

研究Kuramoto-Sivashinsky方程的两种初边值问题,运用Galerkin方法给出一系列先验估计结果,得到广义解和古典解的存在唯一性、正则性及某些条件下的渐近性质。     

Interaction of four rarefaction waves in the bi-symmetric class of the pressure-gradient system

The global existence and structure of solutions to multi-dimensional pressure-gradient system has some open problems. In this paper, we construct global classical solutions to the interaction of four planar rarefaction waves with two axes of symmetry for the pressure-gradient system in two space dimensions. The bi-symmetric initial data is a basic type of four-wave two-dimensional Riemann problems. The solutions in this case are continuous, bounded and self-similar.     

Finite dimensional approximation to solutions of minimization problems in functional spaces

In this paper we consider minimization problems whose objectives are defined on functional spaces. The integral global optimization technique is applied to characterize a global minimum as the limit of a sequence of approximating solutions on finite dimensional subspaces. Necessary and sufficient optimality conditions are presented. A variable measure algorithm is proposed to find such approximating solutions. Examples are presented to illustrate the variable measure method     

A Smoothing Method of Global Optimization that Preserves Global Minima

A new smoothing method of global optimization is proposed in the present paper, which prevents shifting of global minima. In this method, smoothed functions are solutions of a heat diffusion equation with external heat source. The source helps to control the diffusion such that a global minimum of the smoothed function is again a global minimum of the cost function. This property, and the existence and uniqueness of the solution are proved using results in theory of viscosity solutions. Moreover, we devise an iterative equation by which smoothed functions can be obtained analytically for a class of cost functions. The effectiveness and potential of our method are then demonstrated with some experimental results.     

三维Boussinesq方程组大解的全局L~2稳定性

对三维有界及无界区域上的Boussinesq方程的全局L~2稳定性进行了讨论.在解满足适当的条件下,证明了此解为稳定的,并得出此稳定性条件的等价性条件,最后得出了二维Boussinesq方程组在三维扰动下的解的全局存在性和稳定性.     

Global existence and large-time behavior of a parabolic phase-field model with Neumann boundary conditions

In this paper, we continue to study an initial boundary value problems to a model describing the evolution in time of diffusive phase interfaces in sea ice growth. In a previous paper, the global existence and the large-time behavior of weak solutions in one space was studied under Dirichlet boundary conditions. Here, we show that the global existence of weak solutions and the large-time behavior are also studied under Neumann boundary condition. In this paper, we study in space dimension lower than or equal to 3.     

The self-similar solutions of the one-dimensional semilinear Tricomi-type equations

In this article we investigate the issue of existence of global in time solutions of semilinear Tricomi-type equations. We give conditions that relate the nonlinearity, the speed of propagation, and the order of singularities of initial data. These conditions guarantee existence of global in time solutions. In particular, we prove existence of solutions invariant under dilation by solving the Cauchy problem with initial data which are homogeneous functions.