Moving finite element methods for time fractional partial differential equations

With the aim of simulating the blow-up solutions, a moving finite element method, based on nonuniform meshes both in time and in space, is proposed in this paper to solve time fractional partial differential equations (FPDEs). The unconditional stability and convergence rates of 2-α for time and r for space are proved when the method is used for the linear time FPDEs with α-th order time derivatives. Numerical examples are provided to support the theoretical findings, and the blow-up solutions for the nonlinear FPDEs are simulated by the method.     

一类具大初值的半线性抛物方程组的生存跨度

The paper deals with heat equations coupled via exponential nonlinearities. We are interested in the life span(or blow-up time) and obtain the maximal existence time of blow-up solutions. Our proof is based on the comparison principle and Kaplan’s method.     

Theorems of Main Boundedness Type, Derivations and Module Derivations

The study of automatic continuity for Banach algebras rests heavily on threetechnical results, namely the main boundedness theorem (cf. [1] and [2]),stability of separating spaces and finiteness of discontinuous points (Lemma1. 6 and Theorem 2.3 in [3]. It has long been asked whether the last two results     

收缩投影法与涉及Hemi-相对相对非扩张映象的广义平衡问题的强收敛性

Motivated by the recent result obtained by Takahashi and Zembayashi in 2008,we prove a strong convergence theorem for finding a common element of the set of solutions of a generalized equilibrium problem and the set of fixed points of a hemi-relatively nonexpansive mapping in a Banach space by using the shrinking projection method.The main results obtained in this paper extend some recent results.     

Some remarks on holomorphic functions and taylor series in C

Some previous results on convergence of Taylor series in C^n [3] are improved by indicating outside the domain of convergence the points where the series diverges and simplifying some proofs. These results contain the Cauchy-Hadamard theorem in C. Some Cauchy integral formulas of a holomorphic function on a closed ball in C^n are constructed and the Taylor series expansion is deduced.     

BLOW-UP OF THE SOLUTION FOR A KIND OF HIGHER ORDER HYPERBOLIC EVOLUTION SYSTEMS

In this paper, we give some results on the blow-up behaviors of the solution to the mixed problem for some higher nonlinear hyperbolic evolution equation in finite time. By introducing the "blow-up factor K(u,ut)" we get some new results, which generalize the conclusions of [3] and [4].     

BLOW-UP RATE OF POSITIVE SOLUTION OF UNIFORMLY PARABOLIC EQUATIONS WITH NONLINEAR BOUNDARY CONDITIONS

This paper deals with the blow-up of positive solutions of the uniformly pa-rabolic equations ut = Lu + a(x)f(u) subject to nonlinear Neumann boundary conditions . Under suitable assumptions on nonlinear functi-ons f, g and initial data U0(x), the blow-up of the solutions in a finite time is proved by the maximum principles. Moreover, the bounds of "blow-up time" and blow-up rate are obtained.     

具加权非局部源反应扩散方程解的渐近行为（英文）

In this paper,we deal with the blow-up property of the solution to the diffusion equation u_t = △u + a(x)f(u) ∫_Ωh(u)dx,x∈Ω,t0 subject to the null Dirichlet boundary condition.We will show that under certain conditions,the solution blows up in finite time and prove that the set of all blow-up points is the whole region.Especially,in case of f(s) = s~p,h(s) = s~q,0 ≤ p≤1,p + q 1,we obtain the asymptotic behavior of the blow up solution.     

On Alternating Sequences Relative to a c-Matching of a Hypergraph

In[1], C.Berge has modified Theorem 1 of [2]to a theorem which is a charac-terization of maximum c-Matchings in a hypergraph (see[1], P.416, Theorem 2),and at the same time can be considered as a generalization of Berge's theorem on     

Exact Blow-up Solutions forMultidimensional Landau--Lifshitz Equations

We present exact blow-up solutions for multidimensional Landau-Lifshitz equations. It isshown that for any prescribed blow-up time there are exact C-solutions which are blow-up atthe blow-up time and that the solutions are smooth except at the blow-up time.In 1986, Zhou and Guo in [3] proved the global existence of weak solution for generalizedLandau-Lifshitz equations without Gilbert term in multidimensions. They consider the homogeneous boundary problemwith the initial value conditionfor …     

A short note about exposed points in real banach spaces

We express the set of exposed points in terms of rotund points and non-smooth points.As long as we have Banach spaces each time＂bigger＂,we consider sets of non-smooth points each time＂smaller＂.     

CQ Method for Generalized Mixed Equilibrium Problem and Fixed Point Problem of Infinite Family of Quasi--asymptotically Nonexpansive Mappings in Banach Spaces

In this paper, we prove a strong convergence theorem for finding a common element of the set of solutions for a generalized mixed equilibrium problems, the set of fixed points of infinite family of quasi- C-asymptotically non-expansive mappings in a Banach space by using the CQ method. Our results improve the main results of Takahashi and Takahashi and Takahashi and Zembayashi. Moreover, the method of proof adopted in the paper is different from that of them.     

Hilbert空间中涉及一类新的具误差迭代程序的平衡问题的黏性逼近法

In this paper, we introduce an iterative scheme with error by the viscosity approximation method for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of a nonexpansive mapping in a Hilbert space. A strong convergence theorem is given, which generalizes all the results obtained by S.Takahashi and W.Takahashi in 2007. In addition, some of the methods applied in this paper improve those of S.Takahashi and W.Takahashi.     

The structure on invariant measures of <Emphasis Type="Italic">C</Emphasis><Superscript>1</Superscript> generic diffeomorphisms

Let Λ be an isolated non-trivial transitive set of a C 1 generic diffeomorphism f ∈ Diff (M ). We show that the space of invariant measures supported on Λ coincides with the space of accumulation measures of time averages on one orbit. Moreover, the set of points having this property is residual in Λ (which implies that the set of irregular+ points is also residual in Λ). As an application, we show that the non-uniform hyperbolicity of irregular+ points in Λ with totally 0 measure (resp., the non-uniform hyperbolicity of a generic subset in Λ) determines the uniform hyperbolicity of Λ.     

CHARACTERIZATION THEOREM OF GENERALIZED POLYNOMIAL OF BEST APPROXIMATION HAVING BOUNDED COEFFICIENTS

Let the set of generalized polynomials having bounded coeffiicients be K={p=sum from j=1 to n α_j g_j α_j≤α_j≤β,j=1, 2,…, n}, where g_1, g_2,…, g_n are linearly independent continuous functions defined on theinterval [a,b], α_j β_j are extended real numbers satisfying α_j< ∞, β_j>-∞, andα_j≤β_j. Assumethat f is a continuous function defined on a compact set X [a, b]. This paper gives the characterizationtheorem for p being the best uniform approximation to f from K, and points out that the characteri-zation theorem can be applied in calculating the approximate solution of best approximation to f fromK.     

CALDER6N-ZYGMUND OPERAORS ON THE HARDY SPACES OF WEIGHTED HERZ TYPE

Applying the decomposition theorems in [1] and [2] , we obtain the boundedness theorem of Calderbn-Zygmund operator of type 6 on the Hardy spaces of weighted Herz type and establish interpolation theorem of linear operators on the weighted Herz spaces. -     

Banach Upper Density Recurrent Points of C~0-flows

Let X denote a compact metric space with distance d and F:X×R→X or F_t :X→X denote a C~0-flow.From the point of view of ergodic theory,all important dynamical behaviors take place on a full measure set.The aim of this paper is to introduce the notion of Banach upper density recurrent points and to show that the closure of the set of all Banach upper density recurrent points equals the measure center or the minimal center of attraction for a C~0-flow.Moreover,we give an example to show that the set of quasi-weakly almost periodic points can be included properly in the set of Banach upper density recurrent points,and point out that the set of Banach upper density recurrent points can be included properly in the set of recurrent points.     

非局部抛物型方程解的性质

In this short note, we investigate the properties of positive solutions for some non-local parabolic equations. The conditions on the global existence and blow-up in finite time of solution are given.     

EXCURSIONS AND LVY SYSTEM OF BOUNDARY PROCESS

In this paper, the authors investigate the joint distribution of end points of excursion away from a closed set straddling on a fixed time and use this result to compute the Levy system and the Dirichlet form of the boundary process.     

Bubbling solutions of fourth order mean field equations on S4

In this paper, we first establish the existence of blow-up solutions with two antipodal points of the fourth order mean field equations on S⁴. Moreover, we construct non-axially symmetric solutions with blow-up points at the vertices of regular configurations, i.e., equilateral triangles on a great circle, regular tetrahedrons,cubes, octahedrons, icosahedrons and dodecahedrons. The bubbling rates of these blow-up solutions rely on various bubbling configurations.