Local Harnack Inequality for Porous Medium Equation with Convection

In this paper we consider the following problem where the summation convention is used. We call the equation as porous medium equation with convection. Let u = u(x,t) be a continuous weak solution of the equation in Rn × (0 ,T] for some T> 0. Then we can establish BCP estimates and the intrinsic Harnack inequality for the solution of the equation just as the standard equation discussed by other authors previously. This work lay a main foundation of studying other properties of this problem further.     

Homogenization of a nonlinear degenerate parabolic equation

1 Introduction a Let T > 0 and Ω be a bounded open set of R n with Lipschitz boundary ? Ω and let ? Ω = Γ 1 ∪ Γ2 with 1 H n? ( Γ1) > 0, we consider the homogenization of the mixed boundary value problem of the following equation set: 1 2 0 ( ) div ( , , , ) ( , ) ( , ) in (0, ), ( , , , ) 0 on (0, ), on (0, ), ( ,0) in , t b u a x t u u g xu f x t T a x tu u v T u h T u x u ε ε ε ε ε ε ε ε ε ε ε Ω ε εΓ Γ Ω ??? ? ? ? = ?? × ??? ? = × ? ??? = =× ?? (1) where v is the…     

OSCILLATORY CRITERIA FOR A CLASS OF EVEN ORDER NONLINEAR FUNCTIONAL DIFFERENTIAL EQUATION

<正> In this paper we consider the following nth order nonlinear functional differential equation x~(n)(t)+integral from n=1 to ∞p(t,ξ)f(x(t),x[g(t,ξ)])do(ξ)=0(n even,n≧2,b>a) (1) Oscillations of this equation are studied.We make the     

含有双参数的非局部反应扩散方程的奇摄动问题

1 Introduction A kind of problems for ordinary differentialequations with two small parameters has been studiedin [1 -4] and a class of singularly perturbed reaction-diffusion equations has been studied in [5 -6] . Untilnow, few papers discussed the partial differentialequation with two small parameters .Now we considera class of non-local reaction-diffusion equations involv-ing two parameters as follows : u t-(εL1u μL2u) =f(x,u,Tu) , 0 相似文献   

关于四阶微分方程周期边值问题

本文用上下解方法与单调迭代法相结合 ,证明了四阶微分方程周期边值问题 ,u( 4 ) - 2mu″=f(t,u ,u″ -mu) (m >0 )u( 0 ) =u( 2π) ,u′( 0 ) =u′( 2π) ,u″( 0 ) =u″( 2π) .u ( 0 ) =u ( 2π)的解的存在性 ,推广和改进了文〔1〕的结果。     

二维守恒律方程四块常数的黎曼问题Guckenheimer解

1 Introduction Consider scalar conservation laws in two spacedi mensionsut f(u)x g(u)y=0 , (1)wheref(u) ,g(u) satisfies the conditions (1)f(u) ,g(u)∈C3(R) ; (2)f″(u)≠0 ,(u-u0)g″(u) >0 ; (3)gf″″((uu))′≠0 ,and the Riemann problemu(0 ,x,y) =u0(θ) ,0≤θ≤2π, (2)whereθis a polar angle in the (x,y)-plane andu0(θ) is a piecewise constant function. For the sakeof definiteness and si mplicity, we might assumef(u) ,g(u)∈C3(R1) ,f″(u) >0 , ug″(u) >0 ,fg″″((uu))′>0 (H)as well .The exi…     

The homogenization of a class of degenerate quasilinear parabolic equations

1. Introduction and main results 1.1 Introduction Let 0T> and nW be an open bounded domain with with Lipschitz boundary, consider the following initial-boundary value problem : () 0div (,,)(,) in (0,)(,)0 on (0,) (0,)|()tTtuuftTPutTuuxeeeeeWWeeW-==?洞=xaxxxin the space [0,;]pXLTV=, where 1,0(,)pVWemW= is a weighted Sobolev space, p is a constant larger than 1, and e is a positive constant, t and x are variables of the functions a and u. The degenerati…     

一个拟线性两点边值问题存在唯一性定理

在f(t,x),fx(t,x)α（t),α′（t),β（t)连续,fx(t,x)≥-β（t）,β（t）≤π^2 [α^2(t)-2α′(t)]/4,且β(t)≠π^2 [α^2(t)-2α′(t)]/4条件下,证明了拟线性两点边值问题x″=α(t)x′ f(t,x),x(0=a,x(1)=b,对于任给实数a,b都有唯一解。     

Banach空间积-微分方程两点边值问题的解

利用混合单调算子理论及一个新的比较定理讨论了Banach空间积-微分两点边值问题{-u″=f(t,u,Tu,Su),au(0)-bu′(0)=x0,cu(1) du′(1)=x1.解的存在唯一性,其中a,b,c,d≥0,δ=ac ad bc,I=[0,1],x0,x1 ∈ E且f∈C[I×E×E×E,E],Tu(t)=∫0k(t,s)u(s)ds,Su(t)=∫01h(t,s)u(s)ds,(V)t∈I,k∈C(D,R ),D={(t,s)∈I×I,t≥s},h∈C(I×I,R ),R =[0,∞).     

Rudiment of weak Doi-Hopf π-modules

The notion of weak Doi-Hopfπ-datum and weak Doi-Hopfπ-module are given as generalizations of an ordinary weak Doi-Hopf datum and weak Doi-Hopf module introduced in （Boehm, 2000）, also as a generalization of a Doi-Hopfπ-module introduced in （Wang, 2004）. Then we also show that the functor forgetting action or coaction has an adjoint. Furthermore we explain how the notion of weak Doi-Hopfπ-datum is related to weak smash product. This paper presents our preliminary results on weak Doi-Hopf group modules.     

定积分∫bxsin/（x2）dx近似计算需求计算公式的建立

介绍了利用新的函数来求解定积分的近似值,详细阐述了该积分近似计算方法的优点及计算过程,定量的数值计算表明,该方法可获得很高的精确度。换言之,借助于计算机运算,几乎能将该积分的近似值很容易地转换成精确值,因此,它为工程设计中此类积分的近似计算提供了新的科学依据。     

有限区间上单个守恒律整体弱熵解研究

使用折线逼近法,构造了有限区间上非凸单个守恒律初边值问题的整体近似解,并证明其收敛到初边值问题的整体弱熵解.     

有限区间上单个守恒律整体弱熵解研究

使用折线逼近法,构造了有限区间上非凸单个守恒律初边值问题的整体近似解,并证明其收敛到初边值问题的整体弱熵解.     

三维分数阶对流色散方程的数值解法

对一个在有限范围内含有变系数的三维分数阶对流色散方程进行对流项与扩散项施行不同的近似处理,从而构建一种交替方向的隐式Euler方法求解该方程,并探讨该方法的稳定性、相容性和收敛性,最后给出一个含有准确解的数值例子以验证该方法的有效性.     

基于分治法和分支限界法的大规模TSP算法

利用分治法能够处理大规模问题但精度较低,分支限界法能够得到精确解但时间复杂度很高的优点,设计一种有效的基于分治法和分支限界法的大规模TSP求解方法.该算法利用聚类和凸包技术将大规模问题逐层进行有效划分,直到适合分支限界法求解的最佳规模;然后用分支限界法求出每个子问题和每层子问题间的最优解,合并而得到整个问题的解.比较实验表明:该算法在求解质量、稳定性和时间效率上有明显优势.     

统计物理中熵的定义

本文在阐明统计物理熵的定义的基础上,采用了一种便于接受的数学推理证明统计物理中定义的熵与热力学中定义的熵是同一个物理量.     

一种基于Parzen窗技术和Tsallis熵原理的图像分割新方法

提出了一种基于Parzen窗技术和Tsallis熵原理的图像分割新方法．该方法采用Parzen窗技术来估计图像灰度值的空间概率分布,再结合Tsallis熵来构造新的目标函数,最后在图像灰度值范围内搜索使该目标函数达到最大值的灰度值作为最佳全局阈值．通过和传统的基于Tsallis熵理论的图像分割方法相比较,结果表明该方法对图像分割精度非常高,且稳定性强．     

基于模糊等价关系随机变量的联合熵

将概率分布引入到模糊近似空间中,建立模糊概率近似空间,并将Shannon熵进行了推广,给出了模糊概率近似空间的熵,条件熵.同时,讨论了两个模糊等价关系的联合熵及性质.     

基于模糊等价关系的随机变量的条件熵

通过在模糊近似空间中引入概率分布,建立模糊概率近似空间.同时将度量事件集不确定性的shannon熵进行推广,给出了模糊概率近似空间的熵,最后给出了模糊概率近似空间的条件熵及其性质.     

求解强非线性振动方程的改进Duhamal积分方法(英文)

本文提出了一种求解强非线性振动方程的方法 -修正的DUHAMAL积分方法 ,文中证明了所得解的准确度几乎与精确解的相同 ,所给例证表明对所有强非线性问题都是有效的 ,即便是非线性系数趋于无穷大也是如此。