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MULTI-VALUED TOTALLY QUASI-φ-ASYMPTOTICALLY NONEXPANSIVE SEMI-GROUPS AND STRONG CONVERGENCE THEOREMS IN BANACH SPACES
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作者 张石生 王林 赵云河 《Acta Mathematica Scientia》 SCIE CSCD 2013年第2期589-599,共11页
The purpose of this article is first to introduce the concept of multi-valued to- tally Quasi-φ-asymptotically nonexpansive semi-groups, which contains many kinds of semi- groups as its special cases, and then to mod... The purpose of this article is first to introduce the concept of multi-valued to- tally Quasi-φ-asymptotically nonexpansive semi-groups, which contains many kinds of semi- groups as its special cases, and then to modify the Halpern-Mann-type iteration algorithm for multi-valued totally Quasi-cS-asymptotically nonexpansive semi-groups to have the strong convergence under a limit condition only in the framework of Banach spaces. The results presented in this article improve and extend the corresponding results announced by many authors recently. 展开更多
关键词 Multi-valued totally Quasi-q^-asymptotically nonexpansive semi-groups mod-ified Halpern-Mann-type iteration multi-valued quasi-qS-symptotically nonex-pansive semi-groups multi-valued quasi-~b-nonexpansive semi-groups multi-valued relatively nonexpansive semi-groups generalized projection
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Strong convergence theorems for nonexpansive semi-groups in Banach spaces 被引量:2
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作者 张石生 杨莉 柳京爱 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2007年第10期1287-1297,共11页
Some strong convergence theorems of explicit composite iteration scheme for nonexpansive semi-groups in the framework of Banach spaces are established. Results presented in the paper not only extend and improve the co... Some strong convergence theorems of explicit composite iteration scheme for nonexpansive semi-groups in the framework of Banach spaces are established. Results presented in the paper not only extend and improve the corresponding results of ShiojiTakahashi, Suzuki, Xu and Aleyner-Reich, but also give a partially affirmative answer to the open questions raised by Suzuki and Xu. 展开更多
关键词 nonexpansive semi-group demi-closed principle common fixed point uni-formly smooth Banach space weakly continuous normalized duality mapping
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Convergence theorem of common fixed points for Lipschitzian pseudo-contraction semi-groups in Banach spaces
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作者 张石生 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2009年第2期145-152,共8页
The purpose of this paper is to study the weak convergence problems of the implicity iteration process for Lipschitzian pseudocontractive semi-groups in the general Banach spaces. The results presented in this paper e... The purpose of this paper is to study the weak convergence problems of the implicity iteration process for Lipschitzian pseudocontractive semi-groups in the general Banach spaces. The results presented in this paper extend and improve the corresponding results of some people. 展开更多
关键词 Lipschitzian pseudo-contraction semi-group demi-closed principle common fixed point Opial condition strongly pseudo-contraction mapping implicit iteration process
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A Modified Transitional Korteweg-De Vries Equation: Posed in the Quarter Plane
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作者 Charles Bu 《Journal of Applied Mathematics and Physics》 2024年第7期2691-2701,共11页
This paper is concerned with a modified transitional Korteweg-de Vries equation ut+f(t)u2ux+uxxx=0, (x,t)∈R+×R+with initial value u(x,0)=g(x)∈H4(R+)and inhomogeneous boundary value u(0,t)=Q(t)∈C2([ 0,∞ )). Un... This paper is concerned with a modified transitional Korteweg-de Vries equation ut+f(t)u2ux+uxxx=0, (x,t)∈R+×R+with initial value u(x,0)=g(x)∈H4(R+)and inhomogeneous boundary value u(0,t)=Q(t)∈C2([ 0,∞ )). Under the conditions either 1) f(t)≤0, f′(t)≥0or 2) f(t)≤−αwhere α>0, we prove the existence of a unique global classical solution. 展开更多
关键词 Modified Transitional KdV Equation Initial-Boundary Value Problem semi-group Local and Global Existence
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WentzeI-Freidlin Estimates for Jump Processes in Semi-Group Theory: Upper Bound
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作者 Remi Leandre 《Computer Technology and Application》 2011年第4期329-332,共4页
Large deviations estimates for Poisson processes estimate the logarithm of rare events associated to a Poisson process which has more and more jump which are smaller and smaller. In stochastic analysis, they are valid... Large deviations estimates for Poisson processes estimate the logarithm of rare events associated to a Poisson process which has more and more jump which are smaller and smaller. In stochastic analysis, they are valid on the whole path space. Asoociated to this jump process is a Markov semi-group. We translate in semi group theory the proof of Wentzel-Freidlin for these estimates by translating in semi-group theory some basical tools of stochastic analysis as the exponential martingales of stochastic analysis. These Wentzel-Freidlin estimates (upper-bound) are only true for the semi-group. 展开更多
关键词 Large deviations poisson processes semi-groups.
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Global attractor of 2D autonomous g-Navier-Stokes equations 被引量:4
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作者 姜金平 王小霞 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2013年第3期385-394,共10页
In this paper, the existence of global attractors for the 2D autonomous g- Navier-Stokes equations on multi-connected bounded domains is investigated under the general assumptions of boundaries. The estimation of the ... In this paper, the existence of global attractors for the 2D autonomous g- Navier-Stokes equations on multi-connected bounded domains is investigated under the general assumptions of boundaries. The estimation of the Hausdorff dimensions for global attractors is given. 展开更多
关键词 global attractor g-Navier-Stokes equation bounded absorbing set semi-group multi-connected bounded domain Hausdorff dimension
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Asymptotically Antiperiodic Solutions for a Nonlinear Differential Equation with Piecewise Constant Argument in a Banach Space
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作者 William Dimbour Vincent Valmorin 《Applied Mathematics》 2016年第15期1726-1733,共8页
In this paper, we give sufficient conditions for the existence and uniqueness of asymptotically w-antiperiodic solutions for a nonlinear differential equation with piecewise constant argument in a Banach space when w ... In this paper, we give sufficient conditions for the existence and uniqueness of asymptotically w-antiperiodic solutions for a nonlinear differential equation with piecewise constant argument in a Banach space when w is an integer. This is done using the Banach fixed point theorem. An example involving the heat operator is discussed as an illustration of the theory. 展开更多
关键词 Asymptotically ω-Antiperiodic Functions Differential Equations with Piecewise Constant Argument semi-group
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Growing Sandpile Problem with Local and Non-Local Boundaries Conditions
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作者 Urbain Traoré 《Journal of Applied Mathematics and Physics》 2021年第10期2414-2429,共16页
In this paper, we study a class of Prigozhin equation for growing sandpile problem subject to local and a non-local boundary condition. The problem is a generalized model for a growing sandpile problem with Neumann bo... In this paper, we study a class of Prigozhin equation for growing sandpile problem subject to local and a non-local boundary condition. The problem is a generalized model for a growing sandpile problem with Neumann boundary condition (see <a href="#ref1">[1]</a>). By the semi-group theory, we prove the existence and uniqueness of the solution for the model and thanks to a duality method we do the numerical analysis of the problem. We finish our work by doing numerical simulations to validate our theoretical results. 展开更多
关键词 SANDPILE COLLAPSING AVALANCHE Nonlinear semi-group Nonlocal Boundary Conditions Euler Discretization in Time Time Dependent Gradient Constraints
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DEGENERATE SEMI-GROUP METHODS FOR THE EXPONENTIAL STABILITY OF THE FIRST ORDER SINGULAR DISTRIBUTED PARAMETER SYSTEMS 被引量:13
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作者 Zhaoqiang GE Guangtian ZHU Dexing FENG 《Journal of Systems Science & Complexity》 SCIE EI CSCD 2008年第2期260-266,共7页
Exponential stability of the first order singular distributed parameter systems is discussedin the light of degenerate semi-group methods,which is described by the abstract developing equationin Hilbert space.The nece... Exponential stability of the first order singular distributed parameter systems is discussedin the light of degenerate semi-group methods,which is described by the abstract developing equationin Hilbert space.The necessary and sufficient conditions concerning the exponential stability of thefirst order singular distributed parameter systems are given. 展开更多
关键词 Degenerate semi-group exponential stability first order singular distributed parameter systems.
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On a non-autonomous reaction-convection diffusion model to study the bacteria distribution in a river 被引量:1
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作者 Imene Meriem Mostefaoui Ali Moussaoui 《International Journal of Biomathematics》 2017年第6期25-49,共25页
In this paper, we propose a non-autonomous convection-reaction diffusion system (CDI) with a nonlinear reaction source function. This model refers to the quantification and the distribution of antibiotic resistant b... In this paper, we propose a non-autonomous convection-reaction diffusion system (CDI) with a nonlinear reaction source function. This model refers to the quantification and the distribution of antibiotic resistant bacteria (ARB) in a river. The main contributions of this paper are: (i) the determination of the limit set of the system by applying the semigroups theory, it is shown that it is reduced to the solutions of the associated elliptic system (CDI)e, (ii) sufficient conditions for the existence of a positive solution of (CDI)e based on the Leray-Schauder's degree theory. Numerical simulations which support our theoretical analysis are also given. 展开更多
关键词 Reaction-diffusion systems steady states problems degree theory semi-groups.
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