一类带临界指数增长的椭圆型方程组两个正解的存在性

该文主要讨论带临界指数的椭圆型方程组{-Δu + a(x)u =2α/α+βuα-1vβ + f(x),x ∈Ω,-Δv+b(x)v=2β/α+βuαvβ-1+ g(x),x ∈ Ω,(*)u ＞ 0,v ＞ 0,x ∈Ω,u=v=0,x ∈(a)Ω解的存在性,其中Ω是RN中一个光滑有界区域,N=3,4,a≥2,β≥2...     

关于并行迭代区域分解算法的松弛因子

1引言考虑二阶椭圆型Dirichlet边值问题的弱形式,求u∈H_0~1(Ω)使得a(u,v)=(f,v),(?) v∈H_0~1(Ω),(1)其中Ω是平面多角形区域,f∈L~2(Ω),(f,v)=∫_Ωfvdx,a(u,v)=∫_Ω(sum from i,j=1 to 2 a_(ij)(?)u/(?)x_i(?)等 a_0uv)dx,其中[a_(ij)]在Ω上对称一致正定,a_(ij)在Ω上分片连续有界,a_0≥0．由Lax-Milgram引理,问题(1)在H_0~1(Ω)中有唯一解．     

具边界反馈时滞的粘弹方程的能量衰减(英文)

考虑如下具边界反馈时滞的粘弹方程ut(x,t)-Δu(x,t)+∫0tg(t-s)Δu(x,s)ds=0,x∈Ω,t0,u(x,t)=0,x∈Γ0,t0,?u /?v=∫0tg(t-s)/vu(s)ds-μ1ut(x,t)-μ2ut(x,t-τ),x∈Γ1,t0,u(x,0)=u0(x),ut(x,0)=u1(x),x∈Ω,ut(x,t-τ)=f0(x,t-τ),x∈Ω,0tτ,其中Ω∈Rn(n≥1)是具C2类边界Ω的有界域.此外,g是所谓的"记忆核",μ1,μ2是两个实数,τ为时滞.在假设|μ2|μ1下,通过构造合适的Lyapunov函数,证明上述问题能量的一般衰减性,使得指数型衰减和多项式衰减仅仅是其特殊情况.     

认真当好一个医生

考虑如下具边界反馈时滞的粘弹方程ut(x,t)-Δu(x,t)+∫0tg(t-s)Δu(x,s)ds=0,x∈Ω,t>0,u(x,t)=0,x∈Γ0,t>0,?u /?v=∫0tg(t-s)/vu(s)ds-μ1ut(x,t)-μ2ut(x,t-τ),x∈Γ1,t>0,u(x,0)=u0(x),ut(x,0)=u1(x),x∈Ω,ut(x,t-τ)=f0(x,t-τ),x∈Ω,0相似文献   

退缩拟线性椭圆型方程某类边值问题的无穷多解

文[1]证明了如下D氏问题 -D_i(g|Du|~2)D_iu=f(x,u),x∈Ω, u=0,x∈Ω存在非平凡解,本文讨论上述方程的另一类边界问题 -D_i(g|Du|~2)D_iu=f(x,u),x∈Ω, g(|Du|~2)D_iu(0)(n,x_i)+h(x,u)=0,x∈Ω, (1)其中Ω∈R~n是具有光滑边界的有界区域,n(x)是Ω在x点的外法向,D_iu=u/x_i,Du=gradu=u,重复指标表示求和,与问题(1)相应的泛函为:     

一类非线性抛物方程的反问题

本文讨论了下述反问题 u_1-△u=β(t)f(u) γ(x,t),x∈Ω,0相似文献   

振动方程混合有限元方法的后处理

1引 言 考虑下面的振动方程混合问题 u_u+△~2u=f, (x,t)∈Ω×(0,T], u_1(x,0)=w_0,u(x,0)=u_0,x∈Ω, (1.1) u=u/γ=0, (x,t)∈Ω×(0,T],其中ΩR~2为有界规则区域,Ω为其逐段光滑的边界,u/γ表示u沿Ω的外法向导数,T>0为常数,f∈L~2(Ω)为已知函数。 引入涡度函数v=△u,则(1.1)改写为     

一类带弱奇异核非线性偏积分微分方程的全离散有限元

1引言我们将研究下面一类带弱奇异核非线性偏积分微分方程的数值解:u_t-▽·(a(u)▽u)-integral from n=0 to tβ(t-s)△u(s)ds=f(u),x∈Ω,t∈(?),(1.1) u(·,t)=0,x∈(?)Ω,t∈J,(1.2) u(·,0)=v(x),x∈Ω,(1.3)其中Ω为平面上的凸角域,J=(0,T],α和f为R上的光滑函数,满足0相似文献   

关于Schwarz交替法的拟边界松弛方法

§1.松弛方法 我们讨论二阶自共轭椭圆型方程的Dirichlet问题.设Ω?R~2为一多边形区域. a(u,v)=(f,v),v∈H_0~1(Ω),f∈H~(-1)(Ω), u∈H_0~1(Ω)是定义在其上的边值问题的变分形式,这里取齐次边界条件仅为叙述问题方便.双线性型a(·,·)满足:     

三维光滑区域上Navier-Stokes方程的有限元方法

§1.引言设Ω是R~3中的有界区域,且属于C~2.v是正常数.已知:当f∈(L~2(Ω))~3.且||f||0充分小时,Navier—Stokes方程的解存在且唯一.另外,u∈(H~2(Ω)∩H_1~0(Ω))~3,P∈H~1(Ω)\R. 最近,Bernardi讨论三维多面体区域Ω上Stokes方程的有限元解法.有限元空间由分片多项式(关于u为分片特殊三次多项式,关于p为分片常数)构成,进行误差估计时.要求u∈(H~2(Ω)∩H_0~1(Ω))~3,P∈H~1(Ω)\R.当Ω为二维区域上的凸多角形时,Stokes     

连续型指数差分布

本文提出了一个连续型随机变量的概率分布:指数差分布。讨论了该分布的极值、拐点、数学期望和方差,推导了参数的矩估计公式,探讨了该分布与指数分布的关系,给出了该分布在药代动力学中的应用。     

Confluent Form of the Multistep ɛ‐Algorithm,and the Relevant Integrable System

In this paper, the confluent form of the multistep ? ‐algorithm is proposed. The molecule solution of this system is derived by using determinantal identities. A new continuous prediction algorithm based on this confluent form is constructed. It also shows that this algorithm is a special case of the extended Lotka–Volterra system.     

On the constructive characterization of threshold functions

In this paper, the structure of the set of threshold functions and complexity problems are considered. The notion of the signature of a threshold function is defined. It is shown that if a threshold function essentially depends on all of its variables, then the signature of this function is unique. The set of threshold functions is partitioned into classes with equal signatures. A theorem characterizing this partition is proved. The importance of the class of monotone threshold functions is emphasized. The complexity of transferring one threshold function specified by a linear form into another is examined. It is shown that in the worst case this transfer would take exponential time. The structure of the set of linear forms specifying the same threshold function is also examined. It is proved that for any threshold function this set of linear forms has a unique basis in terms of the operation of addition of linear forms. It is also shown that this basis is countable.     

求解多孔介质中可压缩混溶驱动问题的一类满足极大值原理的数值方法

多孔介质中可压缩混溶驱动问题是用非线性抛物型方程组来描述的．用Ｐｏｔｅｍｐａ格式求其数值解．证明了构造的求解方法满足极大值原理，从而可以保证饱和度的数值解在［０，１］范围内这一物理特性，同时还得到了解的收敛性．     

Application of multilevel analysis in animal sciences

Multilevel modeling is considerably useful way to analyze hierarchical data sets. The main purpose of this paper is to apply multilevel analysis in animal science and also show that this modeling technique is appropriate to analyze this kind of data. Thus multilevel modeling technique is used to analyze the milk yield data which has hierarchical structures, sires nested within cows. As a result of the analysis done in this paper, it is obvious that multilevel modeling is needed to use for analyzing this data. This illustrates that it is a convenient way to use multilevel analysis for the data which obtained from animals when the data have hierarchies.     

Limit boundary conditions for finite volume approximations of some physical problems

In the industrial context, finite volume schemes are used to compute an approximation of the solution of a system of equations set on a certain domain. When this domain is bounded, some numerical boundary conditions have to be implemented in order to complete the computation of the finite volume scheme. This is a tricky step in the elaboration of the scheme, which is still not mastered. In fact, at a closer sight, it appears that there is a deep interaction between the understanding of the physical phenomena at the boundary of the domain and the implementation of the numerical boundary conditions. Unfortunately, this link is not always completely intelligible and a reason for this lack of clarity is the fact that, whereas the continuous equation satisfied by the limit of the numerical solution is known, the boundary conditions satisfied by this very limit are not well-understood. The purpose of this paper is to clarify this point in three industrial situations of one-dimensional two-phase flows.     

离散型指数差分布

本文提出了一个离散型概率分布:指数差分布,推导了该分布的最可能成功次数、数学期望和方差,探讨了该分布与几何分布的关系,给出了该分布在马尔可夫链模型中的应用。     

参激白噪声作用下蔡电路的脉冲控制

考察了参激白噪声和脉冲信号联合作用下蔡电路的渐近P阶矩稳定性问题,得到该随机脉冲系统的比较系统,从而可由该确定性比较系统的稳定性得到原随机脉冲系统的渐近P阶矩稳定性.并从理论上得到能使该随机脉冲系统渐近P阶矩稳定的参数取值范围,即在稳定区域内取值的参数组合能够用脉冲方法对该随机蔡电路实现混沌控制.最后用数值仿真验证了理论结果的正确性.     

关于复合材料单层板裂纹尖端的J积分

该文采用复变函数方法,通过将裂纹尖端的应力和位移代入J积分的一般公式,推出了线弹性正交异性复合材料单层板受对称载荷作用的非弹性主方向的裂纹尖端犑积分的复形式－ 复变函数积分的实部,证明了该J积分的路径无关性,得到了它的具体计算公式     

Une étude mathématique d'un modèle de Rotenberg

In this paper, a cell proliferation model of Rotenberg is mathematically studied. Each cell of this population is distinguished by its degree of maturity μ and its maturation velocity v. We equipped this mathematical model by boundary conditions wich generalize all biological rules imposed by Rotenberg. We show that this model is governed by a strongly continuous semigroup. We also develop some properties of this semigroup and we study its asymptotic behaviour in the uniform topology.