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1.
In this paper,we estimate the dimension of the global attractor for nonlinear dissipative Kirchhoff equation in Hilbert spaces
H
01×L
2(Ω) and D(A)×H
01(Ω). Using rescaling technology and linear variation method, we obtain the upper bound for its Hausdorff and fractal dimensions. 相似文献
2.
WANG Meng CHEN Jiecheng & FAN Dashan Department of Mathematics Zhejiang University 《中国科学A辑(英文版)》2006,49(1):98-108
We study certain square functions on product spaces Rn × Rm, whose integral kernels are obtained from kernels which are homogeneous in each factor Rn and Rm and locally in L(log L) away from Rn × {0} and {0} × Rm by means of polynomial distortions in the radial variable. As a model case, we obtain that the Marcinkiewicz integral operator is bounded on Lp(Rn × Rm)(P > 1) for Ω∈ e Llog L(Sn-1 × Sm-1) satisfying the cancellation condition. 相似文献
3.
Xiao-nlng Lin Hong Wang Da-qing Jiang 《应用数学学报(英文版)》2007,23(2):289-302
This paper is devoted to the study ofthe existence of single and multiple positive solutions forthe first order boundary value problem x′= f(t,x),x(0)=x(T),where f ∈ C([0,T]×R).In addition,weapply our existence theorems to a class of nonlinear periodic boundary value problems with a singularity at theorigin.Our proofs are based on a fixed point theorem in cones.Our results improve some recent results in theliteratures. 相似文献
4.
Let {Ln(A,λ)(x)}n≥0 be the sequence of monic Laguerre matrix polynomials defined on [0, ∞) by Ln(A,λ)(x)=n!/(-λ)n∑nk=0(-λ)κ/k!(n-1)! (A I)n[(A I)k]-1 xk,where A ∈ Cr×r. It is known that {Ln(A,λ)(x)}n≥0 is orthogonal with respect to a matrix moment functional when A satisfies the spectral condition that Re(z) > - 1 for every z ∈σ(A).In this note we show that forA such that σ(A) does not contain negative integers, the Laguerre matrix polynomials Ln(A,λ) (x) are orthogonal with respect to a non-diagonal SobolevLaguerre matrix moment functional, which extends two cases: the above matrix case and the known scalar case. 相似文献
5.
Anibal Rodriguez‐Bernal Bixiang Wang Robert Willie 《Mathematical Methods in the Applied Sciences》1999,22(18):1647-1669
In this paper, we establish the global fast dynamics for the time‐dependent Ginzburg–Landau equations of superconductivity. We show the squeezing property and the existence of finite‐dimensional exponential attractors for the system. In addition we prove the existence of the global attractor in L2 × L2 for the Ginzburg–Landau equations in two spatial dimensions. Copyright © 1999 John Wiley & Sons, Ltd. 相似文献
6.
Zhu Xuexian 《分析论及其应用》1989,5(3):83-92
We show that if K(x,y)=Ω(x,y)/|x|n|y|m is a Calder n-Zygmund kerned on Rn×Rm, where Ω∈L2(Sn−1×Sm−1) and b(x,y) is any bounded function which is radial with x∈Rn and y∈Rm respectively, then b(x,y)K(x,y) is the kernel of a convolution operator which is bounded on Lp(Rn×Rm) for 1<p<∞ and n≧2, m≧2.
Project supported by NSFC 相似文献
7.
Yong-ping Liu Gui-qiao XuDepartment of Mathematics Beijing Normal University Beijing China Department of Mathematics Tianjin Normal Univesity Tianjin . China 《应用数学学报(英文版)》2002,18(4):663-674
The classes of the multivariate functions with bounded moduli on Rd and Td are given and their average σ-widths and non-linear n-widths are discussed. The weak asymptotic behaviors are established for the corresponding quantities. 相似文献
8.
In this paper, we consider the global existence, uniqueness and L
∞ estimates of weak solutions to quasilinear parabolic equation of m-Laplacian type u
t
− div(|∇u|
m−2∇u) = u|u|
β−1 ∫Ω |u|
α
dx in Ω × (0,∞) with zero Dirichlet boundary condition in tdΩ. Further, we obtain the L
∞ estimate of the solution u(t) and ∇u(t) for t > 0 with the initial data u
0 ∈ L
q
(Ω) (q > 1), and the case α + β < m − 1. 相似文献
9.
Supposing the smooth involution of the DOLD manifoldP(1,2l) satisfies the following condition: the fiberation π:P(1,2l)×
T×(−1)S∞→RP(∞) is totally nonhomologous to zero (cf. [1, p373]), this paper determines the classification of smooth involution on
the DOLD manifoldP(1,2l) totally.
Supported by the Foundation of Tian Yuan and the Natural Science Foundation of Hebei province. 相似文献
10.
Let (v,u×c,λ)-splitting BIBD denote a (v,u×c,λ)-splitting balanced incomplete block design of order v with block size u×c and index λ. Necessary conditions for the existence of a (v,u×c,λ)-splitting BIBD are v≥uc, λ(v−1)≡0 (mod c(u−1)) and λ
v(v−1)≡0 (mod (c
2
u(u−1))). We show in this paper that the necessary conditions for the existence of a (v,3×3,λ)-splitting BIBD are also sufficient with possible exceptions when (1) (v,λ)∈{(55,1),(39,9k):k=1,2,…}, (2) λ≡0 (mod 54) and v≡0 (mod 2). We also show that there exists a (v,3×4,1)-splitting BIBD when v≡1 (mod 96). As its application, we obtain a new infinite class of optimal 4-splitting authentication codes. 相似文献
11.
We consider the asymptotic behavior of solutions of an infinite lattice dynamical system of dissipative Zakharov equation. By introducing new weight inner product and norm in the space and establishing uniform estimate on "Tail End" of solutions, we overcome some difficulties caused by the lack of Sobolev compact embedding under infinite lattice system, and prove the existence of the global attractor; then by using element decomposition and the covering property of a polyhedron in the finite-dimensional space, we obtain an upper bound for the Kolmogorov ε-entropy of the global attractor; finally, we present the upper semicontinuity of the global attractor. 相似文献
12.
Shu-Yu Hsu 《Mathematische Annalen》2003,325(4):665-693
We prove that the solution u of the equation u
t
=Δlog u, u>0, in (Ω\{x
0})×(0,T), Ω⊂ℝ2, has removable singularities at {x
0}×(0,T) if and only if for any 0<α<1, 0<a<b<T, there exist constants ρ0, C
1, C
2>0, such that C
1
|x−x
0|α≤u(x,t)≤C
2|x−x
0|−α holds for all 0<|x−x
0|≤ρ0 and a≤t≤b. As a consequence we obtain a sufficient condition for removable singularities at {∞}×(0,T) for solutions of the above equation in ℝ2×(0,T) and we prove the existence of infinitely many finite mass solutions for the equation in ℝ2×(0,T) when 0≤u
0∉L
1
(ℝ2) is radially symmetric and u
0L
loc
1(ℝ2).
Received: 16 December 2001 / Revised version: 20 May 2002 / Published online: 10 February 2003
Mathematics Subject Classification (1991): 35B40, 35B25, 35K55, 35K65 相似文献
13.
Some Conditions for Matrices over an Incline To Be Invertible and General Linear Group on an Incline 总被引:2,自引:0,他引:2
Song Chol HAN Hong Xing LI 《数学学报(英文版)》2005,21(5):1093-1098
Inclines are the additively idempotent semirings in which products are less than or equal to either factor. In this paper, some necessary and sufficient conditions for a matrix over L to be invertible are given, where L is an incline with 0 and 1. Also it is proved that L is an integral incline if and only if GLn(L) = PLn (L) for any n (n 〉 2), in which GLn(L) is the group of all n × n invertible matrices over L and PLn(L) is the group of all n × n permutation matrices over L. These results should be regarded as the generalizations and developments of the previous results on the invertible matrices over a distributive lattice. 相似文献
14.
Jouko Tervo 《Israel Journal of Mathematics》1988,63(1):41-66
The paper considers a boundary value problem with the help of the smallest closed extensionL
∼ :H
k →H
k
0×B
h
1×...×B
h
N
of a linear operatorL :C
(0)
∞
(R
+
n
) →L(R
+
n
)×L(R
n−1)×...×L(R
n−1). Here the spacesH
k (the spaces ℬ
h
) are appropriate subspaces ofD′(R
+
n
) (ofD′(R
n−1), resp.),L(R
+
n
) andC
(0)
∞
(R
+
n
)) denotes the linear space of smooth functionsR
n
→C, which are restrictions onR
+
n
of a function from the Schwartz classL (fromC
0
∞
, resp.),L(R
n−1) is the Schwartz class of functionsR
n−1 →C andL is constructed by pseudo-differential operators. Criteria for the closedness of the rangeR(L
∼) and for the uniqueness of solutionsL
∼
U=F are expressed. In addition, ana priori estimate for the corresponding boundary value problem is established. 相似文献
15.
Sheng Fan ZHOU Qiu Li JIA Wei SHI 《数学学报(英文版)》2007,23(2):313-320
We obtain an estimate of the upper bound for Kolmogorov's ε-entropy for the bounded sets with small "tail" in discrete spaces, then we present a sufficient condition for the existence of a global attractor for dissipative lattice systems in a reflexive Banach discrete space and establish an upper bound of Kolmogorov's ε-entropy of the global attractor for lattice systems. 相似文献
16.
Matthias Büger 《Mathematische Nachrichten》2001,222(1):31-78
We examine the autonomous reaction–diffusion system with Dirichlet boundary conditions on (0, 1), where α, β are real, α > 0, and g is C1 and satisfies some conditions which we need in order to prove the existence of solutions. We construct a solution of (RD) for every initial value in L2((0, 1)) × L2((0, 1)), we show that this solution is uniquely determined and that the solution has C∞–smooth representatives for all positive t. We determine the long time behaviour of each solution. In particular, we show that each solution of (RD) tends either to the zero solution or to a periodic orbit. We construct all periodic orbits and show that their number is always finite. It turns out that the global attractor is a finite union of subsets of L2 × L2, which are finite–dimensional manifolds, and the dynamics in these sets can be described completely. 相似文献
17.
Hongjun YUAN 《数学年刊B辑(英文版)》2007,28(4):475-498
The aim of this paper is to study the continuity of weak solutions for quasilinear degenerate parabolic equations of the form U_t-Δφ(u)=O, whereφ■C~1(R~1)is a strictly monotone increasing function.Clearly,the above equation has strong degeneracy,i.e.,the set of zero points ofφ′(·)is permitted to have zero measure. This is an answer to an open problem in[13,p.288]. 相似文献
18.
R. A. McCoy 《Mathematica Slovaca》2010,60(4):541-570
We introduce a lower semicontinuous analog, L
−(X), of the well-studied space of upper semicontinuous set-valued maps with nonempty compact interval images. Because the elements
of L
−(X) contain continuous selections, the space C(X) of real-valued continuous functions on X can be used to establish properties of L
−(X), such as the two interrelated main theorems. The first of these theorems, the Extension Theorem, is proved in this Part
I. The Extension Theorem says that for binormal spaces X and Y, every bimonotone homeomorphism between C(X) and C(Y) can be extended to an ordered homeomorphism between L
−(X) and L
−(Y). The second main theorem, the Factorization Theorem, is proved in Part II. The Factorization Theorem says that for binormal
spaces X and Y, every ordered homeomorphism between L
−(X) and L
−(Y) can be characterized by a unique factorization. 相似文献
19.
Xingyu Yang 《NoDEA : Nonlinear Differential Equations and Applications》2011,18(3):273-285
We consider the global attractor for the weakly damped forced KdV equation in Sobolev spaces [(H)\dot]s(T){\dot{H}^s({\mathbf T})}for s < 0. Under the assumption that the external forcing term belongs to [(L)\dot]2(T),{\dot{L}^2({\mathbf T}),} we prove the existence of the global attractor in [(H)\dot]s(T){\dot{H}^s({\mathbf T})} for −1/2 ≤ s < 0, which is identical to the one in [(L)\dot]2(T){\dot{L}^2({\mathbf T})} and thus is compact in H
3(T). The argument is a combination of the I-method and decomposing the solution into two parts, one of which is uniformly bounded
in [(L)\dot]2(T){\dot{L}^2({\mathbf T})} and the other decays exponentially in [(H)\dot]s(T){\dot{H}^s({\mathbf T})}. 相似文献
20.
LetA generate a strongly continuous contraction semigroup {T(t)} on a Hilbert space and letL be a bounded operator. IfL(ζI−A)−1 is compact, then the Cesàro limit of ‖LT(t)f‖2 (ast→∞) is computed for all vectorsf. This limit is interpreted in terms of bound and scattered states in the context of quantum mechanical and classical wave
propagation problems.
Partially supported by a NSF grant. 相似文献