积分微分方程有限元逼近的强超收敛性

考虑下面的抛物型积分微分方程初边值问题: 　（a） ut+A（t）u+∫0tB（t,s）u（s）ds=f, （x,t）∈Q=Ω×J,J=（0,T] （b） u=0,（x,t）∈　Ω×J,（1） （c）　u（x,0）=u0,x∈Ω,其中Ω为Rd（d≤4）中具有分片光滑边界　Ω的有界域,A（t）是一致正定的二阶椭圆微分算子     

W0^1p（x） Versus C^1 Local Minimizers for a Functional with Critical Growth

Let Ω IR^N, （N ≥ 2） be a bounded smooth domain, p is Holder continuous on Ω^-,
1 〈 p^- ：= inf pΩ（x） ≤ p＋ = supp（x） Ω〈∞,
and f：Ω^-× IR be a C^1 function with f（x,s） ≥ 0, V （x,s） ∈Ω × R^＋ and sup ∈Ωf（x,s） ≤ C（1＋s）^q（x）, Vs∈IR^＋,Vx∈Ω for some 0〈q（x） ∈C（Ω^-） satisfying 1 〈p（x） 〈q（x） ≤p^＊ （x） -1, Vx ∈Ω ^- and 1 〈 p^- ≤ p^＋ ≤ q- ≤ q＋. As usual, p＊ （x） = Np（x）/N-p（x） if p（x） 〈 N and p^＊ （x） = ∞- if p（x） if p（x） 〉 N. Consider the functional I： W0^1,p（x） （Ω） →IR defined as
I（u） def= ∫Ω1/p（x）｜△｜^p（x）dx-∫ΩF（x,u^＋）dx,Vu∈W0^1,p（x）（Ω）,
where F （x, u） = ∫0^s f （x,s） ds. Theorem 1.1 proves that if u0 ∈ C^1 （Ω^-） is a local minimum of I in the C1 （Ω^-） ∩C0 （Ω^-）） topology, then it is also a local minimum in W0^1,p（x） （Ω）） topology. This result is useful for proving multiple solutions to the associated Euler-lagrange equation （P） defined below.     

预估-校正算法跟踪组合内点同伦路径

1.引 言 考虑下列凸数学规划（CNLP）问题 min f（x）,s.t.x ∈ Ω,（1.1）严格可行集合Ω0={x∈Rn:gi（x）<0,i=1,…,m}集合Ω表示Ω0的闭包,f（x）,gi（x）均为充分光滑函数.Ω的边界集合　Ω=Ω\Ω0,g=（g,…,gm）T,　x∈Ω,     

Sobolev方程的基于H~1-Galerkin混合方法的新分裂格式

正1引言考虑如下Sobolev方程u_t-▽·(a(x)▽u_t+a(x)▽u)+u=f(x,t),(x,t)∈Ω×J,u(x,t)=0,(x,t)∈аΩ×J,(1)u(x,0)=u_0(x),x∈Ω.其中Ω是R~d(d=1,2,3)中具有边界     

一类带扰动的非线性椭圆型方程组无穷多弱解的存在性

本文在一定条件讨论了如下一类带扰动项,且被两个Laplacian算子控制的非线性椭圆方程Dirichlet问题无穷多弱解的存在性.（-△u=∣u∣α-1∣υ∣β＋1u＋f,x∈Ω,-△υ=∣u∣α＋1∣υ∣β-1υ＋g,x∈Ω,u（x）＋ υ（x）=0,x∈（e）Ω,）其中-△u：=div（▽u）,（u,υ）∈E：=H10（Ω）× H10（Ω）,（f,g）属于E的对偶空间.     

Regularity of Weak Solutions of Nonlinear Equations with Discontinuous Coefficients

In this paper, we prove that the weak solutions u∈Wloc^1, p （Ω） （1 〈p〈∞） of the following equation with vanishing mean oscillation coefficients A（x）： -div[（A（x）△↓u·△↓u）p-2/2 A（x）△↓u＋│F（x）│^p-2 F（x）]=B（x, u, △↓u）, belong to Wloc^1, q （Ω）（A↓q∈（p, ∞）, provided F ∈ Lloc^q（Ω） and B（x, u, h） satisfies proper growth conditions where Ω ∪→R^N（N≥2） is a bounded open set, A（x）=（A^ij（x）） N×N is a symmetric matrix function.     

关于连续性与一致连续性的一个定理

设f（x）在Ω上连续．任给e〉0，令δ（ε,x0）=1/2sup{δ：当｜x-x0｜〈δ}时，｜f（x）-f（x0）｜〈e},则f（x）在Ω上一致连续的充要条件是δ（e）=inf{δ（ε,x0）：x0∈Ω}〉0.实例给出其应用.     

非局部半线性椭圆型方程奇摄动问题

今考虑如下奇摄动非局部半线性椭圆型方程边值问题：ε为正的小参数，x＝（x1，x2，…，xn）∈Ω，Ω为n维欧氏空间的有界域，Ω为Ω的光滑边界，L＝为Ω上的一致椭圆型算子，为外法向导数．假设：（H1）L的系数及f,g，Ki关于其变元在相应区域内为充分光滑的函数；（H2）fy（x,     

The existence of nontrivial solutions to a semilinear elliptic system on without the ambrosetti-rabinowitz condition

In this paper, we prove the existence of at least one positive solution pair （u, v）∈ H1（RN） × H1（RN） to the following semilinear elliptic system {-△u＋u=f（x,v）,x∈RN,-△u＋u=g（x,v）,x∈RN （0.1）,by using a linking theorem and the concentration-compactness principle. The main conditions we imposed on the nonnegative functions f, g ∈C0（RN× R1） are that, f（x, t） and g（x, t） are superlinear at t = 0 as well as at t =＋∞, that f and g are subcritical in t and satisfy a kind of monotonic conditions. We mention that we do not assume that f or g satisfies the Ambrosetti-Rabinowitz condition as usual. Our main result can be viewed as an extension to a recent result of Miyagaki and Souto [J. Diff. Equ. 245（2008）, 3628-3638] concerning the existence of a positive solution to the semilinear elliptic boundary value problem {-△u＋u=f（x,u）,x∈Ω,u∈H0^1（Ω） where Ω ∩→RN is bounded and a result of Li and Yang [G. Li and J. Yang： Communications in P.D.E. Vol. 29（2004） Nos.5＆ 6.pp.925-954, 2004] concerning （0.1） when f and g are asymptotically linear.     

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   

两不同型部件并联可修系统主算子的性质

研究了两不同型部件并联可修系统.通过选取空间及定义算子A和B,将模型方程转化成了Banach空间中的抽象Cauchy问题.通过分析系统主算子A的谱分布,求出A的谱上界.利用预解正算子及共尾理论,证明了A的谱上界和增长界相等.     

Proofs and surfaces

A formal sequent system dealing with Menelaus' configurations is introduced in this paper. The axiomatic sequents of the system stem from 2-cycles of Δ-complexes. The Euclidean and projective interpretations of the sequents are defined and a soundness result is proved. This system is decidable and its provable sequents deliver incidence results. A cyclic operad structure tied to this system is presented by generators and relations.     

Three-layer finite difference method for solving linear differential algebraic systems of partial differential equations

A boundary value problem is examined for a linear differential algebraic system of partial differential equations with a special structure of the associate matrix pencil. The use of an appropriate transformation makes it possible to split such a system into a system of ordinary differential equations, a hyperbolic system, and a linear algebraic system. A three-layer finite difference method is applied to solve the resulting problem numerically. A theorem on the stability and the convergence of this method is proved, and some numerical results are presented.     

On a Nonlinear Discretized LKR System: Reductions and Underlying Virasoro Symmetry Algebras

A differential-difference version of the Loewner–Konopelchenko–Rogers (LKR) system is constructed by discretization of the spatial variables in the continuous LKR system. The differential-difference LKR system admits a diversity of significant reductions. The symmetry algebras of the discrete LKR system and its reductions are shown to possess underlying Kac–Moody–Virasoro type structure. A discrete dromion-like solution of the LKR system is constructed via finite symmetry group transformation.     

A topological horseshoe in a fractional-order Qi four-wing chaotic system

A fractional-order Qi four-wing chaotic system is present based on the Grunwald-Letnikov denition. The existence of topological horseshoe in a fractional chaotic system is analyzed by utilizing topological horseshoe theory. A Poincare section is properly chosen to obtain the Poincare map which is proved to be semi-conjugate to a 2-shift map, implying that the fractional-order Qi four-wing chaotic system exhibits chaos.     

Simple systems and their higher order self-joinings

The purpose of this work is to study the joinings of simple systems. First the joinings of a simple system with another ergodic system are treated; then the pairwise independent joinings of three systems one of which is simple. The main results obtained are: (1) A weakly mixing simple system with no non-trivial factors with absolutely continuous spectral type is simple of all orders. (2) A weakly mixing system simple of order 3 is simple of all orders.     

Deformation of surfaces in three-dimensional space induced by means of integrable systems

The correspondence between different versions of the Gauss–Weingarten equation is investigated. The compatibility condition for one version of the Gauss–Weingarten equation gives the Gauss–Mainardi–Codazzi system. A deformation of the surface is postulated which takes the same form as the original system but contains an evolution parameter. The compatibility condition of this new augmented system gives the deformed Gauss–Mainardi–Codazzi system. A Lax representation in terms of a spectral parameter associated with the deformed system is established. Several important examples of integrable equations based on the deformed system are then obtained. It is shown that the Gauss–Mainardi–Codazzi system can be obtained as a type of reduction of the self-dual Yang–Mills equations.     

Real-time stable self-learning FNN controller using genetic algorithm

A kind of real-time stable self-learning fuzzy neural network (FNN) control system is proposed in this paper. The control system is composed of two parts: (1) A FNN controller which use genetic algorithm (GA) to search optimal fuzzy rules and membership functions for the unknown controlled plant; (2) A supervisor which can guarantee the stability of the control system during the real-time learning stage, since the GA has some random property which may cause control system unstable. The approach proposed in this paper combine a priori knowledge of designer and the learning ability of FNN to achieve optimal fuzzy control for an unknown plant in real-time. The efficiency of the approach is verified by computer simulation.     

An Asymptotic-Numerical Method for a Class of Weakly Coupled System of Singularly Perturbed Convection-Diffusion Equations

A weakly coupled convection dominated system of m-equations is analyzed. A higher order accurate asymptotic-numerical method is presented. The solutions of convection dominated problem are known to exhibit multi-scale character. There exist narrow region across the boundary of the domain where the solution exhibit steep gradient. This region is termed as boundary layer region and the solution of problem is said to have a boundary layer. Outside of this region, the solution of system behaves smoothly. To capture this multi-scale nature given system is factorized into two explicit systems. The degenerate system of initial value problems (IVPs), obtained by setting ??=?0, corresponds to the smooth solution, which lies outside of boundary layers. For solution inside boundary layers, a system of boundary value problems (BVPs) is obtained using stretching transformation. Regardless of this simple factorization, solutions of these systems preserve the key features of the given coupled system. Runge–Kutta method is used to solve the degenerate system of IVPs, whereas the system of BVPs is solved analytically. Stability and consistency of the proposed method is established. A uniform convergence of higher order is obtained. Possible extension to differential difference equations are also brought to attention. A comparative study of the present method with some state of art existing numerical schemes is carried out by means of several test problems. The results so obtained demonstrate the effectiveness and potential of present approach.     

Stability of equilibrium points of demand-inventory model with stock-dependent demand

A model of demand and inventory of a product in one echelon of supply chain is considered. The model is formulated as a system of difference equations, in which every equilibrium point is nonhyperbolic. A positive invariant set of the system is constructed. An analysis of properties of equilibrium points of the system is based on the Lyapunov method or reducing it to the family of systems of difference equations with hyperbolic equilibrium points.