两相可混溶驱动问题中近似压力方程的一种新方法

1　介　　绍ΩR2为凸多边形区域,Ω上的两相可混溶驱动问题可由以下微分方程系统来描述a)-.[a(x,c)(p-r(c)]=.u=q,b)φ(x)ct+u.c-(Dc)=(c-c)q=g(c),(1.1)其中a(x,c)=-k(x)μ(c),k(x)为介质的渗透率,μ(c)为流体的粘度,p为流体的压力,φ(x)为介质的孔隙度,c为一相流体的体积浓度,q为外部流体的体积流速,且满足相容性条件∫Ωqdx=0.D是2×2阶矩阵,D=φ(x)[dmI+|u|(dlE(u)+dtE⊥(u))],E(u)=(uiuj/|u|2)2×2,dm为分子扩散系数,dl,dt分别为横向、纵向弥散系数.系统的边界条件、初始条件:n为边界单位外法向a)u.n=0,(x,t)∈Ω×Jb)2i,j=1Dij(…     

带有位势的拟线性椭圆型方程正解的存在性

本文利用Ekeland的变分原理及山路引理,研究了以下问题在一定条件下的正解的存在性：{-△pu=λuq/|x|s+ur,u＞0,x∈Ω(∩)RN,{u(x)=0,x∈(a)Ω,其中△pu=div(| ▽ u |p-2 ▽u),u∈W1,p0(Ω),Ω是RN中的有界区域,且0∈Ω,0＜q＜p-1,N≥3,0＜s＜N(p-q-1)p-1 +q+1,p-1＜r≤p*-1,p*=Np(N-p)-1,λ＞0.此时,s可以大于p,从而推广了p=2时的某些结果.     

一类带临界Sobolev指数及有拟超临界Neumann边界条件的椭圆方程正解的多重性

本文讨论了Ω上如下一类带临界增长的椭圆方程在拟超临界的Neumann边界条件下正解的存在性:-Div(| u |p-2 u) =λum up*-1,-| u |p-2 u ν=ψ(x)uq-1,x∈Ω,x∈Ω.这里Ω∈RN,(N≥3)是光滑有界区域, 1≤p < N,0< m < p-1,(N -1)pN - p= p*N-1 ≤q < p*,其中p* =NpN - p是W1,p(Ω)→Ls(Ω)的Sobolev临界指数,p*N-1 =(N -1)pN - p是W1,p(Ω)→Lt( Ω)的在(N-1)维流形上的临界指数,λ>0是一个正参数.     

非线性双曲型方程的混合元方法

1　引　　言考虑下述非线性双曲型方程的混合问题:c(x,u)utt-.(a(x,u)u)=f(x,u,t),　　x∈Ω,t∈J,(1.1)u(x,0)=u0(x),　　x∈Ω,(1.2)ut(x,0)=u1(x),　　x∈Ω,(1.3)u(x,t)=-g(x,t),　　(x,t)∈Ω×J,(1.4)其中ΩR2是一具有Lipschitz边界Ω的有界区域,J=[0,T],0相似文献   

Positive Solution of Nonlinear Elliptic Equation (Critical Exponent Case)

In this paper we study Dirichlet problem: u>0 x∈Ω, u=0 x∈ Ω,Where 1)Ω is a bounded domain in R~n(n≥3),(a_(ij)(x))is positive definite onΩ,a_(ij)(x)∈c~∞(Ω). 2)h(x,u):Ω×(Q,∞)→R is smooth in x,continuous in u,h(x,0)=0 andassume uniformly in x, uniformly in x, and b(x)>0 on Ω.tain the following results.     

Dirichlet零边值问题的正解存在性

由于一些本质困难,N=3被称为具Sobolev临界指数2*的Dirichlet问题-△u=λu+|u|2*-2u,x∈ΩRN;u(x)0,x∈Ω;u=0,x∈Ω的临界维数.众所周知,N=3时,上述问题存在古典(正)解的一个充分条件是Ω为R3上的小球以及14λ1λλ1.本文考虑Ω是R3中更一般的有界光滑区域,得出了一正解存在性结论,从而肯定了沈尧天在文中提及的一个未解决的问题.     

Regularity for solutions to anisotropic obstacle problems

For Ω a bounded subset of R n,n 2,ψ any function in Ω with values in R∪{±∞}andθ∈W1,(q i)(Ω),let K(q i)ψ,θ(Ω)={v∈W1,(q i)(Ω):vψ,a.e.and v-θ∈W1,(q i)0(Ω}.This paper deals with solutions to K(q i)ψ,θ-obstacle problems for the A-harmonic equation-divA(x,u(x),u(x))=-divf(x)as well as the integral functional I(u;Ω)=Ωf(x,u(x),u(x))dx.Local regularity and local boundedness results are obtained under some coercive and controllable growth conditions on the operator A and some growth conditions on the integrand f.     

跳过程的不变分布

设(E，ε)是状态空间，(q(x)，q(x，dy))为保守的q对，即q(x，E)=q(x)，x∈E，π是一严格正的概率测度，满足π(ΩIA)=0，A∈ε．问何时存在q-过程使得π是它的不变分布?本文对q对为全稳定情形，解决了该问题。     

四维空间中一类带奇异位势的非局部临界指数问题的正解

本文研究了如下非局部临界指数问题{(-a+b∫_Ω|?_u|~2dx)△u=μu~3+λ|x|β~/u~(q-1),x∈Ω,x∈δΩ,其中Ω?R~4是一个有界光滑区域且0∈Ω,a≥0,b,λ,μ0,1q2,0β2.利用变分方法,我们获得了一些存在性与多重性结果.     

MULTIPLE NONTRIVIAL SOLUTIONS FOR A CLASS OF SEMILINEAR POLYHARMONIC EQUATIONS

In this paper, we are concerned with the following problem:(-△)ku = λf(x)|u|q-2u + g(x)|u|k*-2u, x ∈Ω,u ∈ Hk0(Ω),where Ω is a bounded domain in RNwith N ≥ 2k + 1, 1 q 2, λ 0, f, g are continuous functions on Ω which are somewhere positive but which may change sign on Ω. k* =2N N-2k is the critical Sobolev exponent. By extracting the Palais-Smale sequence in the Nehari manifold, the existence of multiple nontrivial solutions to this equation is verified.     

裂缝-孔隙介质中地下水污染问题的Galerkin交替方向有限元方法

考虑裂缝 孔隙介质中地下水污染问题均匀化模型的数值模拟．对压力方程采用混合元方法,对浓度方程采用Ｇａｌｅｒｋｉｎ交替方向有限元方法,对吸附浓度方程采用标准Ｇａｌｅｒｋｉｎ方法,证明了交替方向有限元格式具有最优犔２ 和犎１ 模误差估计．     

NUMERICAL METHODS FOR MISCIBLE DISPLACEMENT IN POROUS MEDIA INFLUENCED BY MOBILE WATER AND IMMOBILE WATER

1　ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｒｅｃｅｎｔｙｅａｒｓ,ｔｈｅｉｎｔｅｎｔｉｏｎａｌｏｒａｃｃｉｄｅｎｔａｌｒｅｌｅａｓｅｏｆｔｈｅｃｈｅｍｉｃａｌｗａｓｔｅｓｏｎｓｏｉｌｓｈａｓｆｕｒｔｈｅｒｓｔｉｍｕｌａｔｅｄｃｕｒｒｅｎｔｉｎｔｅｒｅｓｔｓｉｎｔｈｅｍｏｖｅｍｅｎｔｏｆｃｈｅｍｉｃａｌｓ.Ｄｉｓｐｌａｃｅｍｅｎｔｓｔｕｄｉｅｓｈａｖｅｂｅｃｏｍｅｉｍｐｏｒｔａｎｔｔｏｏｌｓｉｎｓｏｉｌｐｈｙｓｉｃｓ,ｐａｒｔｉｃｕｌａｒｌｙｆｏｒｐｒｅｄｉｃｔｉｎｇｔｈｅｍｏｖｅｍｅｎｔｏｆｐｅｓｔｃｉｄｅｓ…     

A combined hybrid mixed element method for incompressible miscible displacement problem with local discontinuous Galerkin procedure

In this article, we propose a combined hybrid discontinuous mixed finite element method for miscible displacement problem with local discontinuous Galerkin method. Here, to obtain more accurate approximation and deal with the discontinuous case, we use the hybrid mixed element method to approximate the pressure and velocity, and use the local discontinuous Galerkin finite element method for the concentration. Compared with other combined methods, this method can improve the efficiency of computation, deal with the discontinuous problem well and keep local mass balance. We study the convergence of this method and give the corresponding optimal error estimates in L^∞(L²) for velocity and concentration and the super convergence in L^∞(H¹) for pressure. Finally, we also present some numerical examples to confirm our theoretical analysis.     

Simulation of spreading surfactant on a thin liquid film

The spreading of insoluble surfactant on a thin liquid film is modeled by a pair of nonlinear partial differential equations for the height of the free surface and the surfactant concentration. A numerical method is developed in which the leading edge of the surfactant is tracked. In the absence of higher order regularization the system becomes hyperbolic/degenerate-parabolic, introducing jumps in the height of the free surface and the surfactant concentration gradient. We compare numerical simulations to those of a hybrid Godunov method in which the height equation is treated as a scalar conservation law and a parabolic solver is used for the surfactant equation. We show how the tracking method applies to the full equations with realistic gravity and capillarity terms included, even though the disturbance in the height of the free surface extends beyond the support of the surfactant concentration.     

海水入侵数值模拟的特征块中心差分法

本文研究二维海水入侵数值模拟的有限差分法．对关于压力的流动方程本文采用块中心差分法,对关于含盐浓度方程的对流扩散方程采用基于完全二次矩形插值的特征差分法,运用先验估计的理论和技巧得到了最佳阶L~2误差估计的结果．     

Concentration of Haar measures, with an application to random matrices

We show that the mixing times of random walks on compact groups can be used to obtain concentration inequalities for the respective Haar measures. As an application, we derive a concentration inequality for the empirical distribution of eigenvalues of sums of random Hermitian matrices, with possible applications in free probability. The advantage over existing techniques is that the new method can deal with functions that are non-Lipschitz or even discontinuous with respect to the usual metrics.     

半导体问题的向后差分配置法及误差分析

Collocation method is put forward to solve the semiconductor problem with heat-conduction, whose mathematical model is described by an initial and boundary problem for a nonlinear partial differential equation system. One elliptic equation is for the electric potential, and three parabolic equations are for the electron concentration, hole concentration and heat-conduction. Using the prior estimate and technique of differential equations, we obtained almost optimal error estimates in L2.     

Acoustic estimation of suspended sediment concentration

In this paper, the acoustic estimation of suspended sediment concentration is discussed and two estimation methods of suspended sediment concentration are presented. The first method is curve fitting method, in which, according to the acoustic backscattering theory we assume that the fitting factor K₁ (r) between the concentration M(r) obtained by acoustic observation and the concentration M₀ ( r) obtained by sampling water is a high order power function of distancer. Using least-square algorithm, we can determine the coefficients of the high order power function by minimizing the difference betweenM( r) and M₀ ( r) in the whole water profile. To the absorption coefficient of sound due to the suspension in water we do not give constraint in the first method. The second method is recursive fitting method, in which we take M₀ ( r) as the conditions of initialization and decision and give rational constraints to some parameters. The recursive process is stable. We analyzed the two methods with a lot of experimental data. The analytical results show that the estimate error of the first method is less than that of the second method and the latter can not only estimate the concentration of suspended sediment but also give the absorption coefficient of sound. Good results have been obtained with the two methods.     

Mixed Method for Compressible Miscible Displacement with Dispersion in Porous Media

Compressible miscible displacement of one fluid by another in porous media is modelled by a nonlinear parabolic system. A finite element procedure is introduced to approximate the concentration of one fluid and the pressure of the mixture. The concentration is treated by a Galerkin method while the pressure is treated by a parabolic mixed finite element method. The effect of dispersion, which is neglected in [1], is considered. Optimal order estimates in L2 are derived for the errors in the approximate solutions.     

多孔介质中可压缩可混溶驱动问题的共轭梯度迭代法的L2模误差估计

2006年3月 高等学校计算数学学报 1数学模型 多孔介质中可压缩可混溶驱动问题的模型是两个非线性抛物型方程:压力方程和饱 和度方程.Douglass和Roberts曾提出其数学模型并研究了半离散化方法[“一”}.袁益让对 此模型研究了特征一有限元方法[s]和差分法10]. 本人对可压缩可混溶驱动问题的模型曾研究了共扼梯度迭代解与原问题真解的最优 阶H‘模误差估计阁.其中饱和度方程的弥散项为一甲·(D(劝甲c)，而本文讨论的是D(司 情况下的尸模误差估计.就护模而言，对此模型目前尚未有人讨论过.从本文可看到， 由于饱和度方程中含有拭c)鬓这一项，…