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Existence and upper semi-continuity of Random Attractors for Nonclassical Diffusion Equation with Multiplicative Noise on Rⁿ

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Journal of Applied Mathematics and Physics 2022年第12期10卷 3898-3919页

作者： Fadlallah Mustafa Mosa Abdelmajid Ali Dafallah Qiaozhen Ma Eshag Mohamed Ahmed Mohamed Y. A. Bakhet Department of Mathematics and Physics Faculty of Education University of Kassala Kassala Sudan Department of Mathematics Faculty of Petroleum and Hydrology Engineering Alsalam University Al-Fulah Sudan College of Mathematics and Statistics Northwest Normal University Lanzhou China Faculty of Pure and Applied Sciences International University of Africa Khartoum Sudan School of Mathematics University of Juba Juba South Sudan

This paper is concerned with the existence and upper semi-continuity of random attractors for the nonclassical diffusion equation with arbitrary polynomial growth nonlinearity and multiplicative noise in H1(Rn). First, we study the existence and uniqueness of solutions by a noise arising in a continuous random dynamical system and the asymptotic compactness is established by using uniform tail estimate technique, and then the existence of random attractors for the nonclassical diffusion equation with arbitrary polynomial growth nonlinearity. As a motivation of our results, we prove an existence and upper semi-continuity of random attractors with respect to the nonlinearity that enters the system together with the noise.

关键词： Random Attractors Nonclassical Diffusion Equations Asymptotic Compactness upper semi-continuity

Existence of Solutions to Generalized Vector Quasi-Equilibrium Problems with Discontinuous Mappings

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Acta Mathematica Sinica,English Series 2006年第4期22卷 1127-1132页

作者： Ya Ping FANG Nan Jing HUANG Department of Mathematics Sichuan University Chengdu 610064 P. R. China

Let X, Y be two finite-dimensional topological vector spaces, Z a Hausdorff topological vector space, K C X and D C Z be two nonempty sets, C be a pointed, closed, and convex cone in Y with int C ≠θ Let S ： K → 2^K and T ： K → 2^D be two multivalued mappings, and φ ： K × D × K → Y be a trifunction. In this paper, we consider the generalized vector quasi-equilibrium problem, which is formulated by finding X∈ K and y∈ T（x） such that x∈ E S（x） and φ（x,y, u）（∈/） -int C for all u ∈ S（x）. We establish an existence result in which T is not supposed to have any continuity property. Our results extend and improve the corresponding results of Cubiotti, Yao and Guo.

关键词： Generalized vector quasi-equilibrium problem upper semi-continuity Lower semi-continuity Fixed point Existence

Attractors for Discrete Nonlinear Schrdinger Equation with Delay

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Acta Mathematicae Applicatae Sinica 2010年第4期26卷 633-642页

作者： Tao Chen Sheng-fan Zhou Cai-di Zhao Admissions and Career Service Shanghai UniversityShanghai 200444China Department of Applied Mathematics Shanghai Normal UniversityShanghai 200234China Department of Mathematics and Information Science Wenzhou UniversityWenzhou 325035China

In this paper,we first prove the existence of the global attractor Aν ∈ C（[-ν,0],2）（ν 0） for a weak damping discrete nonlinear Schrdinger equation with *** we consider an upper semi-continuity of Aν as ν ... 详细信息

关键词： Discrete Schrdinger equation delay global attractor upper semi-continuity

SET VALUE MAPPING AND ITS APPLICATION

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Applied Mathematics and Mechanics(English Edition) 2006年第2期27卷 263-268页

作者：李挺 Department of Mathematics Suzhou University Suzhou 215006 Jiangsu Province P. R. China

The dynamics of set value mapping is considered. For the upper semi-continuous set value maps, the existence of attractors under some conditions and the upper semi-continuity of attractors under the perturbation are proved. Its application in numerical simulation of differential equation is also considered. The upper semi-continuity of attractors in set value maps under the perturbation is used to show the reasonable of subdivision algorithm and interval arithmetic in numerical simulation of differential equation.

关键词： set value mapping attractor upper semi-continuity

Robustness of Pullback Attractors for 2D Incompressible Navier-Stokes Equations with Delay

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Journal of Partial Differential Equations 2024年第1期37卷 25-46页

作者： SU Keqin YANG Xinguang College of Information and Management Science Henan Agricultural UniversityZhengzhou 450046China. Department of Mathematics and Information Science Henan Normal UniversityXinxiang 453007China

This paper is concerned with the pullback dynamics and robustness for the 2D incompressible Navier-Stokes equations with delay on the convective term in bounded *** appropriate assumption on the delay term,we establish the existence of pullback attractors for the fluid flow model,which is dependent on the past *** by the idea in Zelati and Gal’s paper(JMFM,2015),the robustness of pullback attractors has been proved via upper semi-continuity in last section.

关键词： Navier-Stokes equations pullback attractors delay upper semi-continuity

Generalized Well-Posedness and Stability of Solutions in Set Optimization

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Journal of Mathematical Research with Applications 2022年第6期42卷 637-652页

作者： Congjun ZHANG Zhiwei WANG Sai LI School of Applied Mathematics Nanjing University of Finance and Economics Department of Mathematics Nanjing University

The aim of this paper is to investigate the well-posedness and stability in set optimization. The notion of generalized well-posedness for set optimization problems is introduced using the embedding technique for the first time. Some criteria and characterizations of this type of well-posedness are derived. Sufficient conditions are also given for this type of ***, by virtue of a generalized Gerstewitz's function, the equivalent relation between this type of well-posedness and the generalized well-posedness of a scalar optimization problem is established. Finally, the upper semi-continuity and lower semi-continuity of weak efficient solution mappings for parametric set optimization problems are investigated under some suitable conditions.

关键词： well-posedness stability set optimization Gerstewitz's function upper semi-continuity lower semi-continuity

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全直线上反应-扩散方程谱逼近的大时间性态

高等学校计算数学学报 2005年第S1期 188-192页

作者：谌德向新民上海师范大学数理信息学院上海师范大学数理信息学院上海 200234

1 引言及预备知识文[1]研究了如下的全直线上的反应一扩散方程其中γ,λ>0为常数,g(x)∈L2(A),f满足下面的条件

关键词： reaction-diffusion equation global attractor approximate attractor upper semi-continuity

The Hyperspace of the Regions Below of Continuous Maps from the Converging Sequence

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Northeastern Mathematical Journal 2006年第1期22卷 46-54页

作者：杨忠强范玲玲 Department of Mathematics Shantou University Shantou Guangdong Province 515063

Let S = {1,1/2,1/2^2,…,1/∞ = 0} and I = [0, 1] be the unit interval. We use ↓USC（S） and ↓C（S） to denote the families of the regions below of all upper semi-continuous maps and of the regions below of all continuous maps from S to I and ↓C0（S） = {↓f∈↓C（S）： f（0） = 0}. ↓USC（S） endowed with the Vietoris topology is a topological space. A pair of topological spaces （X, Y） means that X is a topological space and Y is its subspace. Two pairs of topological spaces （X, Y） and （A, B） are called pair-homeomorphic （≈） if there exists a homeomorphism h ： X→A from X onto A such that h（Y） = B. It is proved that, （↓USC（S）,↓C0（S）） ≈（Q, s） and （↓USC（S）,↓C（S）／ ↓C0（S））≈（Q, c0）, where Q = [-1,1]^ω is the Hilbert cube and s = （-1,1）^ω,c0= {（xn）∈Q ： limn→∞= 0}. But we do not know what （↓USC（S）,↓C（S））is.

关键词： regions below upper semi-continuity the Hilbert cube pseudo-interior,strongly universal the converging sequence