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51.
Yaryong Heo 《Journal of Mathematical Analysis and Applications》2009,351(1):152-162
For and m>0 we consider the maximal operator given by
52.
Finding an efficient or weakly efficient solution in a multiobjective linear programming (MOLP) problem is not a difficult task. The difficulty lies in finding all these solutions and representing their structures. Since there are many convenient approaches that obtain all of the (weakly) efficient extreme points and (weakly) efficient extreme rays in an MOLP, this paper develops an algorithm which effectively finds all of the (weakly) efficient maximal faces in an MOLP using all of the (weakly) efficient extreme points and extreme rays. The proposed algorithm avoids the degeneration problem, which is the major problem of the most of previous algorithms and gives an explicit structure for maximal efficient (weak efficient) faces. Consequently, it gives a convenient representation of efficient (weak efficient) set using maximal efficient (weak efficient) faces. The proposed algorithm is based on two facts. Firstly, the efficiency and weak efficiency property of a face is determined using a relative interior point of it. Secondly, the relative interior point is achieved using some affine independent points. Indeed, the affine independent property enable us to obtain an efficient relative interior point rapidly. 相似文献
53.
Mark Veraar 《Potential Analysis》2009,30(4):341-370
In this paper we extend certain correlation inequalities for vector-valued Gaussian random variables due to Kolmogorov and Rozanov. The inequalities are applied to sequences of Gaussian random variables and Gaussian processes. For sequences of Gaussian random variables satisfying a correlation assumption, we prove a Borel-Cantelli lemma, maximal inequalities and several laws of large numbers. This extends results of Be?ka and Ciesielski and of Hytönen and the author. In the second part of the paper we consider a certain class of vector-valued Gaussian processes which are α-Hölder continuous in p-th moment. For these processes we obtain Besov regularity of the paths of order α. We also obtain estimates for the moments in the Besov norm. In particular, the results are applied to vector-valued fractional Brownian motions. These results extend earlier work of Ciesielski, Kerkyacharian and Roynette and of Hytönen and the author. 相似文献
54.
Raymond Mortini 《Monatshefte für Mathematik》2009,158(1):81-95
We characterize those sequences (x
n
) in the spectrum of H
∞ whose Nevanlinna–Pick interpolation problems admit thin Blaschke products as solutions. We also study under which conditions
there is a Blaschke product B with prescribed zero-set distribution and solving problems of the form B(x) = f
n
(x) for every x ∈ P(x
n
), where P(x
n
) is the Gleason part associated with the point x
n
and where (f
n
) is an arbitrary sequence of functions in the unit ball of H
∞. As a corollary we get a new characterization of Carleson–Newman Blaschke products in terms of bounded universal functions,
a result first proved by Gallardo and Gorkin.
相似文献
55.
This paper deals with the Cahn–Hilliard equation
subject to the boundary conditions
and the initial condition ψ(0,x) = ψ0(x) where J = (0,∞), and Ω ⊂ ℝ
n
is a bounded domain with smooth boundary Γ = ∂ G, n≤ 3, and Γ
s
,σ
s
,g
s
> 0, h are constants.
This problem has already been considered in the recent paper of R. Racke and S. Zheng (The Cahn–Hilliard equation with dynamic
boundary conditions. Adv. Diff. Eq. 8, 83–110, 2003), where global existence and uniqueness were obtained. In this paper we first obtain results on the maximal
L
p
-regularity of the solution. We then study the asymptotic behavior of the solution of this problem and prove the existence
of a global attractor.
Mathematics Subject Classification (2000) 82C26, 35B40, 35B65, 35Q99 相似文献
56.
Athanassios G. Kartsatos Igor V. Skrypnik 《Transactions of the American Mathematical Society》2006,358(9):3851-3881
Let be a real reflexive Banach space with dual and open and bounded and such that Let be maximal monotone with and and with and A general and more unified eigenvalue theory is developed for the pair of operators Further conditions are given for the existence of a pair such that
The ``implicit" eigenvalue problem, with in place of is also considered. The existence of continuous branches of eigenvectors of infinite length is investigated, and a Fredholm alternative in the spirit of Necas is given for a pair of homogeneous operators No compactness assumptions have been made in most of the results. The degree theories of Browder and Skrypnik are used, as well as the degree theories of the authors involving densely defined perturbations of maximal monotone operators. Applications to nonlinear partial differential equations are included.
The ``implicit" eigenvalue problem, with in place of is also considered. The existence of continuous branches of eigenvectors of infinite length is investigated, and a Fredholm alternative in the spirit of Necas is given for a pair of homogeneous operators No compactness assumptions have been made in most of the results. The degree theories of Browder and Skrypnik are used, as well as the degree theories of the authors involving densely defined perturbations of maximal monotone operators. Applications to nonlinear partial differential equations are included.
57.
研究了一类带有周期边界条件的三维拟抛物粘性扩散方程有限差分解的长时间行为.证明了数值解的存在唯一性,离散系统全局吸引子的存在性,差分格式的长时间稳定性和收敛性.此外,我们给出了上半连续性. 相似文献
58.
Abstract
In this note, we consider a Frémond model of shape memory alloys. Let us imagine a piece of a shape memory alloy which is
fixed on one part of its boundary, and assume that forcing terms, e.g., heat sources and external stress on the remaining
part of its boundary, converge to some time-independent functions, in appropriate senses, as time goes to infinity. Under
the above assumption, we shall discuss the asymptotic stability for the dynamical system from the viewpoint of the global
attractor. More precisely, we generalize the paper [12] dealing with the one-dimensional case. First, we show the existence
of the global attractor for the limiting autonomous dynamical system; then we characterize the asymptotic stability for the
non-autonomous case by the limiting global attractor.
* Project supported by the MIUR-COFIN 2004 research program on “Mathematical Modelling and Analysis of Free Boundary Problems”. 相似文献
59.
本文讨论了一类带调和势|x|^2的非线性Schroedinger方程解的长时间行为,证明了整体吸引子的存在性. 相似文献
60.
Banach空间中极大单调算子零点的带误差项的新迭代格式 总被引:8,自引:0,他引:8
令E为实光滑、一致凸Banach空间,E为其对偶空间,AE×E为极大单调算子且A-10≠Φ.本文将引入新的迭代算法,并利用Lyapunov泛函,Qr算子与广义投影算子等技巧,证明了迭代序列弱收敛于极大单调算子A的零点的结论. 相似文献