LOWER BOUNDS ESTIMATE FOR THE BLOW-UP TIME OF A NONLINEAR NONLOCAL POROUS MEDIUM EQUATION＊

The lower bounds for the blow-up time of blow-up solutions to the nonlinear nolocal porous equation ut=Δum+up∫Ωuqdx with either null Dirichlet boundary condition or homogeneous Neumann boundary conditi...     

OPTIMAL AND SUPERCONVERGENCE ESTIMATES OF THE FIMITE ELEMENT METHOD FOR A SCALAR HYPERBOLIC EQUATION

ＯＰＴＩＭＡＬＡＮＤＳＵＰＥＲＣＯＮＶＥＲＧＥＮＣＥＥＳＴＩＭＡＴＥＳＯＦＴＨＥＦＩＭＩＴＥＥＬＥＭＥＮＴＭＥＴＨＯＤＦＯＲＡＳＣＡＬＡＲＨＹＰＥＲＢＯＬＩＣＥＱＵＡＴＩＯＮＺｈｏｕＡｉｈｕｉ（周爱辉）ＬｉｎＱｕｎ（林群）（Ｉｎｓｔ．ｏｆＳｙｓ．Ｓｃ...     

SINGULAR SOLUTIONS FOR A CONVECTION DIFFUSION EQUATION WITH ABSORPTION

ＳＩＮＧＵＬＡＲＳＯＬＵＴＩＯＮＳＦＯＲＡＣＯＮＶＥＣＴＩＯＮＤＩＦＦＵＳＩＯＮＥＱＵＡＴＩＯＮＷＩＴＨＡＢＳＯＲＰＴＩＯＮＺｈａｏＪｕｎｎｉｎｇ（赵俊宁）（Ｄｅｐｔ．ｏｆＭａｔｈ．，ＪｉｌｉｎＵｎｉｖｅｒｓｉｔｙ，Ｃｈａｎｇｃｈｕｎ１３００２３，Ｃ...     

GLOBAL SUPERCONVERGENCE ESTIMATES OF FINITE ELEMENT METHOD FOR SCHRODINGER EQUATION

1.IntroductionConsiderthefollowinginitialboundaryvalueproblemofSchr6dingerequationwheren~[0,1]',at~On/Ot,T>0isaconstant.Theequivalentvariationalformof(1.1)is:foralltE[0,T],findu(t)6Hi(n)satisfiesthefollowingvariationalequation:where(w,v)~IwvdxdenotestheinnerproductofL'(fl)anda(u,v)~(Vu,Vv),ibetheimaginaryunit.Weassumethatthefunctionsarecomplex--valuedandHibertspacesarecomplexspaces.LetThbeaquasiuniformrectangulationoffiwithmeshsizeh>0andS'(O)CHi(fi)bethecorrespondingpiecewisebilinearpol…     

THE CHEBYSHEV SPECTRAL METHOD WITH A RESTRAINT OPERATOR FOR BURGERS EQUATION

ＴＨＥＣＨＥＢＹＳＨＥＶＳＰＥＣＴＲＡＬＭＥＴＨＯＤＷＩＴＨＡＲＥＳＴＲＡＩＮＴＯＰＥＲＡＴＯＲＦＯＲＢＵＲＧＥＲＳＥＱＵＡＴＩＯＮ￥ＭＡＨＥＰＩＮＧ；ＧＵＯＢＥＮＹＵ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＳｈａｎｇｈａｉＵｎｉｖｅｒｓｉ...     

ASYMPTOTIC BEHAVIOR OF POSITIVE RADIAL SOLUTIONS FOR THE GENERALIZED EMDEN-FOWLER EQUATION WITH APPLICATION

In this paper, we consider a class of semilinear parabolic differential equation where nonlinear term has local bounded coefficients. Under some assumptions, we get the existence and uniqueness of solution. Terminate to the time variable, we obtain the so called generalized Emden-Fowler equation and the asymptotic behavior of positive radial solutions have been given in all dimensions. At the end of this paper, we give its application to critical branching Brownian motion (also called measure-valued branching processes).     

THE MINIMAX DIRECTION FOR THE DIRECT PRODUCT OF A CONVEX CONE WITH ITS APPLICATION TO TESTING PROBLEMS

Let C be a closed convex cone in R~k and let C~p be the p-th direct product of C.Thispaper gives some results of the minimax direction with respect to C~p and an innerproduct based on(?),where is a k×k diagonal matrix with positive diagonalelements,is a p×p positive definite matrix and is the Kronecker product ofand.It is also shown that the results may be applied to test the homogeneity of knormal mean vectors where the mean vectors are restricted by a given partial order.     

CONVERGENCE OF THE DISCONTINUOUS GALERKIN METHOD FOR A SCALAR HYPERBOLIC EQUATION

It is proved in this paper that the approximate solution of the discontinuous Galerkin method does converge even the exact solution of the first order hyperbolic equation is discontinuous.     

A SOBOLEV-HARDY INEQUALITY WITH APPLICATION TO A NONLINEAR ELLIPTIC EQUATION

In this paper, when μ< 1/4, and 2 0 and q=2(3-σ),the method is coming from the idea of Pohozaev.     

A NOTE ON TWO-DIMENSIONAL SYMPLECTIC SCHEME-SHOOTING METHOD FOR SOLVING THE SCHRDINGER EQUATION

The symplectic scheme-shooting method (SSSM) for solving the two-dimensional time-independent Schrodinger equation is presented. The generalized time-independent Schrodinger equation based on the active and cyclic coordinates is evaluated. The procedure of the separation of the active and cyclic coordinates of A2B type molecule (C2(?) symmetry) is given.     

BLOW-UP OF THE SOLUTION FOR A CLASS OF POROUS MEDIUM EQUATION WITH POSITIVE INITIAL ENERGY

This paper deals with a class of porous medium equation ut=△u^m＋f（u）with homogeneous Dirichlet boundary conditions. The blow-up criteria is established by using the method of energy under the suitable condition on the function f（u）.     

求解对流扩散方程的ICT-MMOCAA差分解法

Combing the ideas of FCT^[1,2]with the MMOCAA^[3],the ICT-MMOCAA difference method,in which the transport is corrected by interpolation,is established for convection diffusion problem in the paper,The new method possesses the property of general FCT schemes and it is free from oscillation,with which the large gradient problem is solved by the MMOCAA difference method based on high-order(≥2)Lagrange interpolation^[3].Because the analysis in [3]is only suit for the scheme based on linear interpolation,the analysis method difered form [3] is used for obaining the error estimates of the new method.The numerical example is given in the paper.     

具非线性非局部边界条件的一类多孔介质方程解的整体存在与爆破

本文研究了具有非线性非局部边界条件的一类退化型多孔介质方程.利用比较原理和上下解的方法,获得了方程的解是否在有限时刻爆破或整体存在的准则,这些结果表明,权重函数g(x,y)及指数l的大小对于问题解的爆破与否起着关键的作用.最后研究了爆破解的爆破率.     

线性定常对流占优对流扩散问题的有限体积-流线扩散有限元法

In this paper, two kinds of Finite Volume-Streamline Diffusion Finite Element methods (FV-SD) for steady convection dominated-diffusion problem are presented and the stability and error estimation for the numerical schemes considered are established in the norm stronger than L^2-norm. The theocratical analysis and numerical example show that the schemes constructed in this paper are keeping the basic properties of Streamline Diffusion (SD) method and they are more economical in computing scale than SD scheme, and also, they have same accuracy as FV-Galerkin FE method and better stability than it.     

A TAILORED FINITE POINT METHOD FOR THE HELMHOLTZ EQUATION WITH HIGH WAVE NUMBERS IN HETEROGENEOUS MEDIUM

In this paper, we propose a tailored-finite-point method for the numerical simulation of the Helmholtz equation with high wave numbers in heterogeneous medium. Our finite point method has been tailored to some particular properties of the problem, which allows us to obtain approximate solutions with the same behaviors as that of the exact solution very naturally. Especially, when the coefficients are piecewise constant, we can get the exact solution with only one point in each subdomain. Our finite-point method has uniformly convergent rate with respect to wave number k in L^2-norm.     

ERROR ESTIMATES OF GALERKIN METHOD FOR HIGH DIMENSIONAL STEADY STATE KURAMOTO-SIVASHINSKY EQUATION

1　ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｔｈｅｐａｐｅｒ,ｗｅｃｏｎｓｉｄｅｒｔｈｅｆｏｌｌｏｗｉｎｇＫ -Ｓｅｑｕａｔｉｏｎ (ｆｏｒｅｘａｍｐｌｅ,ｓｅｅ [1 ] -[3]ａｎｄｒｅｆｅｒｅｎｃｅｓｔｈｅｒｅｉｎ)ｉｎｓｐａｃｅｄｉｍｅｎｓｉｏｎ≥ 3:Δ2 ｕ+Δｕ+ 12 ｜ ｕ｜2 -12 Ｎｉ=1ｌｉ∫ＩＮ｜ ｕ｜2 ｄｘ=0 ,ｘ∈ＩＮ,(1 )ｗｉｔｈＬ ｐｅｒｉｏｄｉｃｂｏｕｎｄａｒｙｃｏｎｄｉｔｉｏｎｓ,Ｌ =(ｌ1,ｌ2 ,… ,ｌＮ)ｂｅｉｎｇｔｈｅｓｉｚｅｏｆａｔｙｐｉｃａｌｐａｔｔｅｒｎｃｅｌｌ (ａｌｓｏｂｉｆｕｒｃａｔｉｏｎｐａｒ…     

CONVERGENCE OF NUMERICAL SCHEMES FOR A CONSERVATION EQUATION WITH CONVECTION AND DEGENERATE DIFFUSION

The approximation of problems with linear convection and degenerate nonlinear difFusion,which arise in the framework of the transport of energy in porous media with thermodynamic transitions,is done usingθ-scheme based on the centred gradient discretisation method.The convergence of the numerical scheme is proved,although the test functions which can be chosen are restricted by the weak regularity hypotheses on the convection field,owing to the application of a discrete Gronwall lemma and a general result for the time translate in the gradient discretisation setting.Some numerical examples,using both the Control Volume Finite Element method and the Vertex Approximate Gradient scheme,show the role ofθfor stabilising the scheme.     

裂缝—孔隙介质中地下水污染问题的混合元方法

1 引言 地下水污染问题是一类重要的环境问题.由于地质结构往往是裂缝-孔隙的双重介质,给这类实际问题的数值模拟带来极大困难.本文从描述裂缝-孔隙双重介质的均匀化模型出发,研究问题的数值方法,并对其进行理论分析,对解决地下水污染问题具有重要的 理论和实用意义. 设Ω为R~2中具有光滑边界的有界区域,令J=(0,T].由达西定律和质量守恒原理有以下模型: (1.1) (1.2) (1.3)初边值条件为 (1.4) (1.5)其中p为流体压力,u为Darcy速度,c,c′分别为污染物的浓度和介质表面的吸附浓度,s_1(x),s_2(x)分别为流动水和非流动水中相对贮水率,D为扩散矩阵,为孔隙度,I为单位阵,dm为分子扩散系数,d_l,d_t为纵向和横向弥散系数,a(x)为交换系数,q为源汇项,c~*为源汇项处的浓度值,在q<0处,c~*=c,在q>0处,c~*为源汇项处污染物的已知浓度.γ为的外法向量.相容性条件为|q(x,t)dx=0,x∈Ω,t∈J.