三维Keller-Segel-Navier-Stokes方程弱解的整体存在性

本文证明具有logistic源的一个3维Keller-Segel-Navier-Stokes方程弱解的整体存在性,并研究了弱解的长时间行为.     

一类非线性发展方程整体解的存在性、渐近性与解的爆破

研究一类非线性发展方程初边值问题整体弱解的存在性，渐近性和解的爆破问题，证明在关于非线性项的不同条件下，上述初边值问题分别在大初值和小初始能量的情况下存在整体弱解，并且讨论了弱解的渐近性。还证明：在相反的条件下，上述弱解在有限时刻爆破，并且给出了一个实例。     

三维Keller-Segel-Navier-Stokes方程弱解的整体存在性

本文证明具有logistic源的一个3维Keller-Segel-Navier-Stokes方程弱解的整体存在性，并研究了弱解的长时间行为.     

非等熵气体动力学方程组大初值问题的放缩框架

非等熵气体动力学系统Cauchy问题弱解全局存在性有两个公开问题:一个是包含真空的小初值问题,另一个是任意大初值问题.本文通过引入一个放缩框架证明了上述两个问题的等价性,即对于粘性消失解,其包含真空小初值问题的一致BV估计蕴含着任意大初值问题弱解的全局存在性.该放缩框架对大多数具有物理背景的双曲守恒律系统亦成立.     

趋化NS系统弱解的全局存在性（英文）

本文主要研究趋化NS系统在2维的有界光滑领域Ω?R~2中.本文利用Galerkin方法证明了不可压缩的NS系统弱解的存在性.其次,利用一系列检验程序,证明了带有初边值条件的趋化NS系统弱解的局部存在性,进一步得到该系统弱解的全局存在性.     

多维泛函型随机微分方程的弱解存在性

本文证明了多维泛函型随机微分方程■当系数σ(t,x),b(t,x)关于t可测,关于x连续且满足一般的线性增长条件时的弱解存在性,同时还给出了当b仅可测时方程弱解存在的一个充分条件。     

一种新的固固相变模型的弱解的存在性（英文）

本文研究了一个新的基于构型力的序参数不守恒的相变模型.这个模型由两个线性方程和一个非线性的抛物方程组成.给出了其初边值问题的弱解的一种定义,并在一维情形下证明了弱解的存在性.     

带雪崩项的半导体方程的瞬态解

研究带雪崩项的半导体方程的混合初边值问题．采用逼近过程和先验估计,在一定条件下,证明了该问题整体弱解的存在性或局部弱解的存在性．     

准晶弹性理论边值问题的可解性

通过给出准晶弹性偏微分方程组边值问题的矩阵表示去定义弱解,利用Korn不等式和函数空间理论证明了这种弱解的存在性与唯一性,从而把经典弹性理论边值问题解的存在性定理推广到准晶弹性理论上,这种理论为发展极其复杂与困难的准晶弹性的偏微分方程的边值问题的数值解提供了一个基础．     

一个广义薄膜方程弱解的存在性

讨论一个广义薄膜方程,在一些初值的假定下,用时间离散化方法证明其弱解的存在性.     

Existence of positive periodic solutions of impulsive functional differential equations with two parameters

In this paper, we employ a well-known fixed-point index theorem to study the existence and non-existence of positive periodic solutions for the periodic impulsive functional differential equations with two parameters. Several existence and non-existence results are established.     

The Non-Existence of Maximal Sets of Four Mutually Orthogonal Latin Squares of Order 8

We establish the non-existence of a maximal set of four mols (mutually orthogonal Latin squares) of order 8 and the non-existence of (8, 5) projective Hjelmslev planes. We present a maximal set of four mols of order 9.     

在连续的时间系统中不存在Shilnikov型混沌

在n维的、时间连续的光滑系统中,得到了不存在同宿轨道和异宿轨道的条件.基于此结论并用一个基本实例,推断出如下结论:在多项式常微分方程系统中,有着以不存在同宿轨道和异宿轨道为特征的第4类混沌.     

Non-existence of positive solution to a quasilinear elliptic system and blow-up estimates for a reaction-diffusion system

IntroductionIn these years, the reaction-diffusion systems of Fujita typea5 ttell as the related elliptic systemt'ith fl g RN, Tnl. n1 3 0, i = 1, 2. \vere studied by' a nu111ber of authors. The probiemsconcerning system (l) inc1ude globa1 existence and g1obal existen(.e numbers. b1ow-up. bloxv-uprates, and blow-up sets. uniqueness or nonuniqueness. et('. FOr s}'stem (2) there are problemssuch as existence or non-existence. uniqueness or nonllniqueI1ess. and so ol1. 1Ieanwhile. itseems that…     

Non-existence of positive solutions of some elliptic equations in positive-type domains

In this work we prove a non-existence result for a positive solution of a Dirichlet boundary value problem in a class of domains that are more general than star-shaped ones. Our result extends some earlier non-existence results for the star-shaped case. We also present an example of a domain which satisfies our conditions but not star-shaped essentially.     

Existence and non-existence of solution for semilinear elliptic equation with harmonic potential and Sobolev critical/supercritical nonlinearities

In this paper, we study the existence and non-existence of the positive solution to a semilinear elliptic equation with the harmonic potential and power type nonlinearity. First, we obtain non-existence result in three space dimension with the Sobolev critical nonlinearity. Next, we prove that there exists a global bifurcation branch with the Sobolev supercritical nonlinearity.     

空间形式中子流形的象半径与体积增长

本文讨论空间形式中子流形的象半径及体积增长的估计。作为应用,用γ-平均曲率的语言获得了一个紧致超曲面的不存在性定理,它是经典紧致极小超曲面不存在性定理的推广.     

Non-existence and existence of localized solitary waves for the two-dimensional long-wave–short-wave interaction equations

In this study, we establish the non-existence and existence results for the localized solitary waves of the two-dimensional long-wave–short-wave interaction equations. Both the non-existence and existence results are based on Pohozaev-type identities. We prove the existence of solitary waves by showing that the solitary waves are the minimizers of an associated variational problem.     

A geometric non-existence proof of an extremal additive code

We use a geometric approach to solve an extremal problem in coding theory. Expressed in geometric language we show the non-existence of a system of 12 lines in PG(8,2) with the property that no hyperplane contains more than 5 of the lines. In coding-theoretic terms this is equivalent with the non-existence of an additive quaternary code of length 12, binary dimension 9 and minimum distance 7.     

Non-existence of Some Nearly Perfect Sequences,Near Butson–Hadamard Matrices,and Near Conference Matrices

In this paper we study the non-existence problem of (nearly) perfect (almost) m-ary sequences via their connection to (near) Butson–Hadamard (BH) matrices and (near) conference matrices. We refine the idea of Brock on the unsolvability of certain equations in the case of cyclotomic number fields whose ring of integers is not a principal ideal domain and get many new non-existence results for near BH matrices and near conference matrices. We also apply previous results on vanishing sums of roots of unity and self conjugacy condition to derive non-existence results for near BH matrices and near conference matrices.