具有非线性记忆项的耗散波动方程的整体吸引子

LetΩRn be a bounded domain with a smooth boundary.We consider the longtime dynamics of a class of damped wave equations with a nonlinear memory term utt+αut-△u-∫0t 0μ(t-s)|u(s)| βu(s)ds + g(u)=f.Based on a time-uniform priori estimate method,the existence of the compact global attractor is proved for this model in the phase space H10(Ω)×L2(Ω).     

一类非自治Brinkman-Forchheimer系统的拉回$\mathcal{D}$-吸引子

The asymptotic behavior of solutions of the three-dimensional nonautonomous Brinkman-Forchheimer equation is investigated. And the existence of pullback global attractors in L2 (Ω) and H01(Ω) is proved, respectively.     

GLOBAL WELL-POSEDNESS AND SCATTERING FOR THE MASS-CRITICAL HARTREE EQUATION IN HIGH DIMENSIONS

We obtain global well-posedness and scattering, and global Lt,x2(d+2)/d spacetime bounds for solutions to the defocusing mass-critical Hartree equation in Rt × Rxd, d ≥ 5.     

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.     

The local and global existence of solutions for a generalized Camassa-Holm equation

A fully nonlinear generalization of the Camassa-Holm equation is investigated. Using the pseudoparabolic regularization technique, its local well-posedness in Sobolev space Hs(R) with s3/2 is established via a limiting procedure. Provided that the initial momentum (1-x2)u0 satisfies the sign condition, u0∈Hs(R)(s3/2) and u0∈L1(R),the existence and uniqueness of global solutions for the equation are shown to be true in the space C([0,∞); Hs(R))∩C1([0,∞);Hs-1(R)).     

Problem with Critical Sobolev Exponent and with Weight

The authors consider the problem: -div(p▽u) = uq-1 λu, u > 0 inΩ, u = 0 on (?)Ω, whereΩis a bounded domain in Rn, n≥3, p :Ω→R is a given positive weight such that p∈H1 (Ω)∩C(Ω),λis a real constant and q = 2n/n-2, and study the effect of the behavior of p near its minima and the impact of the geometry of domain on the existence of solutions for the above problem.     

On a Spectral Sequence for Twisted Cohomologies

Let(Ω*(M), d) be the de Rham cochain complex for a smooth compact closed manifolds M of dimension n. For an odd-degree closed form H, there is a twisted de Rham cochain complex(Ω*(M), d + H∧) and its associated twisted de Rham cohomology H*(M, H). The authors show that there exists a spectral sequence {Ep,qr, dr} derived from the filtration Fp(Ω*(M)) = i≥pΩi(M) of Ω*(M), which converges to the twisted de Rham cohomology H*(M, H). It is also shown that the differentials in the spectral sequence can be given in terms of cup products and specific elements of Massey products as well,which generalizes a result of Atiyah and Segal. Some results about the indeterminacy of differentials are also given in this paper.     

保持算子截断的可加映射

Let H be a complex Hilbert space and B(H)the algebra of all bounded linear operators on H.An operator A is called the truncation of B in B(H)if A=P_ABP_A^*,where PA and P_A^*denote projections onto the closures of R(A)and R(A^*),respectively.In this paper,we determine the structures of all additive surjective maps on B(H)preserving the truncation of operators in both directions.     

On quasi-similarity of subnormal operators

For a compact subset K in the complex plane, let Rat(K) denote the set of the rational functions with poles off K. Given a finite positive measure with support contained in K, let R2(K,v) denote the closure of Rat(K) in L2(v) and let Sv denote the operator of multiplication by the independent variable z on R2(K, v), that is, Svf = zf for every f∈R2(K, v). SupposeΩis a bounded open subset in the complex plane whose complement has finitely many components and suppose Rat(Ω) is dense in the Hardy space H2(Ω). Letσdenote a harmonic measure forΩ. In this work, we characterize all subnormal operators quasi-similar to Sσ, the operators of the multiplication by z on R2(Ω,σ). We show that for a given v supported onΩ, Sv is quasi-similar to Sσif and only if v/■Ω■σ and log(dv/dσ)∈L1(σ). Our result extends a well-known result of Clary on the unit disk.     

EXISTENCE OF MINIMISERS FOR A CLASS OF FREE DISCONTINUITY PROBLEMS IN THE HEISENBERG GROUP Hn

The purpose of this paper is to prove existence of minimisers of the functional J(K,u):=∫Ω\K f(Lu)dx α∫Ω\K |u - g|qdx βSQ-1d(K∩Ω),where Ω is an open set of the Heisenberg group Hn, K runs over all closed sets of Hn, u varies in C1H(Ω\K), α,β＞0,q ≥ 1,g ∈ Lq(Ω) ∩L∞(Ω) and f: R2n → R is a convex function satisfying some structure conditions (H1)(H2)(H3) (see below).     

SPECTRAL GAP SOLUTIONS OF THE DISSIPATIVE KIRCHHOFF EQUATION

§1. Introduction This paper is devoted to the question of the global solvability of the dissipative Kirch-ho? equation ?t u ? m 2 | x u|2dx x u δ?tu = 0 (x ∈?, t > 0), …     

Cowen-Douglas算子的交换子

设H是一个可分的Hilbert空间,(?)(H)是H上的有界线性算子全体．对 A∈(?)(H),(?)’(A)={B∈(?)(H):AB=BA},rad(?)’(A)表示(?)’(A)的Jacob son根．本文首先举例说明了存在Cowen-Douglas算子T,商代数(?)’(T)／rad(?)’(T) 可以是不交换的．在给出了使得(?)’(T)／rad(?)’(T)交换的充分条件之后,证明了使得 (?)’(T)／rad(?)’(T)交换的Cowen-Douglas算子在Bn(Ω)中是稠密的．对Bmn(Ω),得到了类似的结果。     

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.     

L~∞-Bounds of Solutions for Strongly Nonlinear Elliptic Problems with Two Lower Order Terms

In this work,we will prove the existence of bounded solutions in W_0~(1,p)(Ω)∩L~∞(Ω) for nonlinear elliptic equations-div(a(x,u,▽u))+g(x,u,▽u)+H(x,▽u) =f,where a,g and H are Caratheodory functions which satisfy some conditions,and the right hand side/belongs to W~(-1,q)(Ω).     

Generalization of tangential trace spaces of H(curl,Ω) for curvilinear Lipschitz polyhedral domains Ω

For curvilinear Lipschitz polyhedral domains Ω, explicit characterizations of the tangential trace spaces of H ¹(Ω) are presented. These extend the original characterizations given by Buffa and Ciarlet that hold on Lipschitz polyhedral domains with plane faces. The tangential trace spaces of H ¹(Ω) are fundamental for the definition, analysis and intuitive understanding of the trace spaces of H ( curl ,Ω) and therefore, more general characterizations of the latter are obtained at the same time. Copyright © 2013 John Wiley & Sons, Ltd.     

一类本质正规算子的稳定不变子空间

在本文中 ,我们给出了一类本质正规算子的稳定不变子空间的特征 .即 ,T∈ L( H2 ( Ω;μ) )且满足1 ) T是本质正规算子 ;2 )σ( T) =Ω,σe( T) = Ω,σp( T) =Ω ;3) ind( T-z) =n,z∈Ω;4 ) minind( T-z) =0 ,z∈ Ω.M是 T的非平凡的不变子空间 ,则 M是 T的稳定不变子空间当且仅当 dim M<∞ and dim M⊥ =∞     

非线性Sobolev-Galpern方程的有限维整体吸引子

本文研究非线性Sobolev-Galpern方程解的渐近性态．首先证明了该方程在H^2(Ω)∩H0^1(Ω)中整体弱吸引子的存在性，然后利用一个能量方程证明了整体弱吸引子实际上是整体强吸引子，建立了整体吸引子的有限维性．     

一个变分不等式的奇异摄动

对变分不等式的奇异摄动问题进行了探索,证明了解的重合集Iε={x∈Ωuε（x)=φ}在Hausdorff距离意义下收敛到ε＝0时解的重合集。     

ON MORTAR-TYPE TRUNC ELEMENT METHOD FOR PLATE BENDING PROBOEM

Ｔｈｉｓｐａｐｅｒｉｓｉｎｔｅｎｄｅｄｆｏｒｐｒｅｓｅｎｔｉｎｇａｍｏｒｔａｒ ｔｙｐｅＴＲＵＮＣｅｌｅｍｅｎｔｍｅｔｈｏｄｆｏｒｓｏｌｖｉｎｇｐｌａｔｅｂｅｎｄｉｎｇｐｒｏｂｌｅｍａｎｄｔｈｅｎｇｉｖｉｎｇｔｈｅｒｅａｌｔｅｄｅｒｒｏｒａｎａｌｙｓｉｓ.Ｔｏｂｅｇｉｎｗｉｔｈ ,ｗｅｒｅｖｉｅｗｓｏｍｅｅｘｉｓｔｉｎｇｒｅｓｕｌｔｓｉｎｔｈｅｃｏｎｔｅｘｔｏｆｍｏｒｔａｒｅｌｅｍｅｎｔｍｅｔｈｏｄｓ.Ｉｎｓｏｍｅｓｅｎｓｅ,ｍｏｒｔａｒｅｌｅ ｍｅｎｔｍｅｔｈｏｄｓｃａｎｂｅｖｉｅｗｅｄａｓｎｏｎｏ…     

临界Hartree方程组基态解的存在性

本文考虑临界耦合的Hartree方程组{-△+λu=∫Ω|u(z)|^2*μ/|x-z|μdz|u|^2*μ-2u+βν,x∈Ω,-△+νu=∫Ω|ν(z)|^2*μ/|x-z|μdz|u|^2*μ-2u+βν,x∈Ω,其中Ω是RN中带有光滑边界的有界区域,N≥3,λ,v是常数,且满足λ,v>-λ1(Ω),λ1(Ω)是(-△,H01(Ω))的第一特征值,β> 0是耦合参数,临界指标2μ*=(2N-μ)/(N-2)来源于Hardy-LittlewoodSobolev不等式,利用变分的方法证明了临界Hartree方程组基态正解的存在性.