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Semigroup of Weakly Continuous Operators Associated to a Generalized Schrödinger Equation
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作者 Yolanda Silvia Santiago Ayala 《Journal of Applied Mathematics and Physics》 2023年第4期1061-1076,共16页
In this work, we prove the existence and uniqueness of the solution of the generalized Schrödinger equation in the periodic distributional space P’. Furthermore, we prove that the solution depends continuously r... In this work, we prove the existence and uniqueness of the solution of the generalized Schrödinger equation in the periodic distributional space P’. Furthermore, we prove that the solution depends continuously respect to the initial data in P’. Introducing a family of weakly continuous operators, we prove that this family is a semigroup of operators in P’. Then, with this family of operators, we get a fine version of the existence and dependency continuous theorem obtained. Finally, we provide some consequences of this study. 展开更多
关键词 Semigroups Theory weakly continuous Operators Existence of Solution Generalized Schrödinger Equation Distributional Problem Periodic Distributional Space
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Group of Weakly Continuous Operators Associated to a Generalized Schrödinger Type Homogeneous Model
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作者 Yolanda Silvia Santiago Ayala 《Journal of Applied Mathematics and Physics》 2023年第4期919-932,共14页
In this work, we prove the existence and uniqueness of the solution of the generalized Schrödinger type homogeneous model in the periodic distributional space P’. Furthermore, we prove that the solution depends ... In this work, we prove the existence and uniqueness of the solution of the generalized Schrödinger type homogeneous model in the periodic distributional space P’. Furthermore, we prove that the solution depends continuously respect to the initial data in P’. Introducing a family of weakly continuous operators, we prove that this family is a group of operators in P’. Then, with this family of operators, we get a fine version of the existence and dependency continuous theorem obtained. Finally, we give some remarks derived from this study. 展开更多
关键词 Groups Theory weakly continuous Operators Existence of Solution Generalized Schrödinger Type Equation Homogeneous Equation Periodic Distributional Space
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Viscosity approximation methods with weakly contractive mappings for nonexpansive mappings 被引量:1
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作者 WANG Ya-qin 《Journal of Zhejiang University-Science A(Applied Physics & Engineering)》 SCIE EI CAS CSCD 2007年第10期1691-1694,共4页
Let K be a closed convex subset of a real reflexive Banach space E, T:K→K be a nonexpansive mapping, and f:K→K be a fixed weakly contractive (may not be contractive) mapping. Then for any t∈(0, 1), let x1∈K ... Let K be a closed convex subset of a real reflexive Banach space E, T:K→K be a nonexpansive mapping, and f:K→K be a fixed weakly contractive (may not be contractive) mapping. Then for any t∈(0, 1), let x1∈K be the unique fixed point of the weak contraction x1→tf(x)+(1-t)Tx. If T has a fixed point and E admits a weakly sequentially continuous duality mapping from E to E^*, then it is shown that {xt} converges to a fixed point of T as t→0. The results presented here improve and generalize the corresponding results in (Xu, 2004). 展开更多
关键词 Viscosity approximation methods weakly contractive mapping Fixed point weakly sequentially continuous duality mapping
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Picosecond supercontinuum generation seeded by a weak continuous wave
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作者 李荧 侯静 +2 位作者 冷进勇 王文亮 姜宗福 《Chinese Physics B》 SCIE EI CAS CSCD 2013年第7期214-217,共4页
We experimentally investigate the spectral details of a picosecond supercontinuum pumped at 1064 nm and seeded by a weak continuous wave (~20000 times weaker than the pulse peak power) at several power levels in ph... We experimentally investigate the spectral details of a picosecond supercontinuum pumped at 1064 nm and seeded by a weak continuous wave (~20000 times weaker than the pulse peak power) at several power levels in photonic crystal fibers. Seeding at different wavelengths leads to different spectral details and the effects to the bandwidth of supercontinuum are also distinct. Spectra can be widened when seeded by a continuous wave at 1070 nm and narrowed by ~100 nm when seeded at 1080 nm. The influence is enhanced by increasing the average seeded power. 展开更多
关键词 supercontinuum seeded by a weak continuous wave modulation instability four-wave mixing
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Fixed Point Theory for 1-Set Weakly Contractive Operators in Banach Spaces
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作者 Shaoyuan Xu Afif Ben Amar 《Analysis in Theory and Applications》 2013年第3期208-220,共13页
In this work, using an analogue of Sadovskii's fixed point result and several important inequalities we investigate and give new existence theorems for the nonlinear operator equation F(x) =μx, (μ≥1) for some... In this work, using an analogue of Sadovskii's fixed point result and several important inequalities we investigate and give new existence theorems for the nonlinear operator equation F(x) =μx, (μ≥1) for some weakly sequentially continuous, weakly condensing and weakly 1-set weakly contractive operators with different boundary conditions. Correspondingly, we can obtain some applicable fixed point theorems of Leray-Schauder, Altman and Furi-Pera types in the weak topology setting which generalize and improve the corresponding results of [3,15,16]. 展开更多
关键词 weakly condensing weakly sequentially continuous fixed point theorem operator equation.
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MEASURES OF WEAK NONCOMPACTNESS AND FIXED POINT THEORY FOR 1-SET WEAKLY CONTRACTIVE OPERATORS ON UNBOUNDED DOMAINS
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作者 ShaoyuanXu Afif Ben Amar 《Analysis in Theory and Applications》 2011年第3期224-238,共15页
The main purpose of this paper is to prove a collection of new fixed point theorems and existence theorems for the nonlinear operator equation F(x) = αx (α≥〉 1) for so-called 1-set weakly contractive operators... The main purpose of this paper is to prove a collection of new fixed point theorems and existence theorems for the nonlinear operator equation F(x) = αx (α≥〉 1) for so-called 1-set weakly contractive operators on unbounded domains in Banach spaces. We also introduce the concept of weakly semi-closed operator at the origin and obtain a series of new fixed point theorems and the existence theorems for the nonlinear operator equation F(x) = αx (α≥1) for such class of operators. As consequences, the main results general- ize and improve the relevant results, which are obtained by O'Regan and A. Ben Amar and M. Mnif in 1998 and 2009 respectively. In addition, we get the famous fixed point theorems of Leray-Schauder, Altman, Petryshyn and Rothe type in the case of weakly sequentially continuous, 1-set weakly contractive (μ-nonexpansive) and weakly semi-closed operators at the origin and their generalizations. The main condition in our results is formulated in terms of axiomatic measures of weak compactness. 展开更多
关键词 measure of weak noncompactness weakly condensing and weakly nonexpansive weakly sequentially continuous weakly semi-closed at the origin fixedpoint theorem
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Holder continuous weak solutions of the 2D Boussinesq equation with thermal diffusion
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作者 Tianwen Luo Tao Tao Liqun Zhang 《Science China Mathematics》 SCIE CSCD 2024年第8期1777-1806,共30页
We show the existence of Holder continuous periodic weak solutions of the 2D Boussinesq equation with thermal diffusion which satisfy the prescribed kinetic energy.More precisely,for any smooth e(t):[0,1]→R+andε∈(0... We show the existence of Holder continuous periodic weak solutions of the 2D Boussinesq equation with thermal diffusion which satisfy the prescribed kinetic energy.More precisely,for any smooth e(t):[0,1]→R+andε∈(0,110),there exist v∈C 110−ε([0,1]×T2)andθ∈C 1,120−εt 2 C 2,1 x 10−ε([0,1]×T2),which satisfy(1.1)in the sense of distribution and e(t)=ˆT2|v(t,x)|2 dx,∀t∈[0,1]. 展开更多
关键词 2D Boussinesq equation with thermal diffusion Holder continuous periodic weak solutions prescribed kinetic energy
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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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ON PROBLEM OF NEAREST COMMON FIXED POINT OF NONEXPANSIVE MAPPINGS
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作者 张石生 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2006年第7期883-889,共7页
The purpose is by using the viscosity approximation method to study the convergence problem of the iterative scheme for an infinite family of nonexpansive mappings and a given contractive mapping in a reflexive Banach... The purpose is by using the viscosity approximation method to study the convergence problem of the iterative scheme for an infinite family of nonexpansive mappings and a given contractive mapping in a reflexive Banach space. Under suitable conditions, it was proved that the iterative sequence converges strongly to a common fixed point which was also the unique solution of some variational inequality in a reflexive Banach space. The results presented extend and improve some recent results. 展开更多
关键词 sequence of nonexpansive mappings viscosity approximation common fixed point demi-closed principle weakly sequentially continuous duality mapping normalized duality mapping
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A Characterization of Weak Sequential Continuity of Lattice Operations on Banach Lattices
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作者 陈滋利 《Journal of Modern Transportation》 2000年第1期1-3,共3页
This paper deals with a characterization for a Banach lattice in which the lattice operations are weakly sequentially continuous. As an application an elementary proof for an important result due to Wickstead is pro... This paper deals with a characterization for a Banach lattice in which the lattice operations are weakly sequentially continuous. As an application an elementary proof for an important result due to Wickstead is provided. 展开更多
关键词 Banach lattice weak sequential continuous Dunford Pettis operator
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The Continuous Selections for the Metric Projection
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作者 宋文华 《Journal of Mathematical Research and Exposition》 CSCD 北大核心 2002年第2期197-204,共8页
Some results concerning weakly continuous selection for set-valued mappingare given and, applied to metric projection. Let Y be a subspace of a Banach space X.If Y is a separable reflexive Banach space,reinoved a firs... Some results concerning weakly continuous selection for set-valued mappingare given and, applied to metric projection. Let Y be a subspace of a Banach space X.If Y is a separable reflexive Banach space,reinoved a first category subset, the metricprojection is weakly lower semicontinnous and admits a weakly continuous selection. 展开更多
关键词 continuous selection metric projection weakly continuous
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Random duality 被引量:3
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作者 GUO TieXin CHEN XinXiang 《Science China Mathematics》 SCIE 2009年第10期2084-2098,共15页
The purpose of this paper is to provide a random duality theory for the further development of the theory of random conjugate spaces for random normed modules. First, the complicated stratification structure of a modu... The purpose of this paper is to provide a random duality theory for the further development of the theory of random conjugate spaces for random normed modules. First, the complicated stratification structure of a module over the algebra L(μ, K) frequently makes our investigations into random duality theory considerably different from the corresponding ones into classical duality theory, thus in this paper we have to first begin in overcoming several substantial obstacles to the study of stratification structure on random locally convex modules. Then, we give the representation theorem of weakly continuous canonical module homomorphisms, the theorem of existence of random Mackey structure, and the random bipolar theorem with respect to a regular random duality pair together with some important random compatible invariants. 展开更多
关键词 random duality weakly continuous canonical module homomorphism random compatible structure random bipolar theorem 46A20 46A16 46H05 46H25
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Strong Convergence Theorems of Viscosity Approximation for Accretive Operators 被引量:4
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作者 YAN Li Xia ZHOU Hai Yun 《Journal of Mathematical Research and Exposition》 CSCD 北大核心 2008年第3期579-588,共10页
Let E be a real Banach space and let A be an m-accretive operator with a zero. Define a sequence {x_n} as follows:x_n+1=α_nf(x_n)+(1-α_n)J_r_n x_n,where {α_n},{r_n} are sequences satisfying certain conditions,and J... Let E be a real Banach space and let A be an m-accretive operator with a zero. Define a sequence {x_n} as follows:x_n+1=α_nf(x_n)+(1-α_n)J_r_n x_n,where {α_n},{r_n} are sequences satisfying certain conditions,and J_r denotes the resolvent(I+rA)^(-1)for r>1.Strong convergence of the algorithm {x_n} is obtained provided that E either has a weakly continuous duality map or is uniformly smooth. 展开更多
关键词 fixed point nonexpansive mapping m-accretive operator viscosity approximation weakly continuous duality map uniformly smooth Banach space.
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Viscosity Approximation Method for Infinitely Many Asymptotically Nonexpansive Maps in Banach Spaces 被引量:2
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作者 Ruo Feng RAO 《Journal of Mathematical Research and Exposition》 CSCD 2011年第4期749-756,共8页
In the framework of reflexive Banach spaces satisfying a weakly continuous duality map, the author uses the viscosity approximation method to obtain the strong convergence theorem for iterations with infinitely many a... In the framework of reflexive Banach spaces satisfying a weakly continuous duality map, the author uses the viscosity approximation method to obtain the strong convergence theorem for iterations with infinitely many asymptotically nonexpansive mappings. The main results obtained in this paper improve and extend some recent results. 展开更多
关键词 asymptotically nonexpansive mapping Gauge function weakly continuous duality map.
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Iteration x_(n+1)=α_(n+1)f(x_n)+(1-α_(n+1))T_(n+1)x_n for an Infinite Family of Nonexpansive Maps {T_n}_(n=1)~∞ 被引量:3
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作者 饶若峰 《Journal of Mathematical Research and Exposition》 CSCD 2009年第4期639-648,共10页
Under the framework of uniformly smooth Banach spaces, Chang proved in 2006 that the sequence {xn} generated by the iteration xn+1 =αn+1f(xn) + (1 - αn+1)Tn+1xn converges strongly to a common fixed point of... Under the framework of uniformly smooth Banach spaces, Chang proved in 2006 that the sequence {xn} generated by the iteration xn+1 =αn+1f(xn) + (1 - αn+1)Tn+1xn converges strongly to a common fixed point of a finite family of nonexpansive maps {Tn}, where f : C → C is a contraction. However, in this paper, the author considers the iteration in more general case that {Tn} is an infinite family of nonexpansive maps, and proves that Chang's result holds still in the setting of reflexive Banach spaces with the weakly sequentially continuous duality mapping. 展开更多
关键词 infinitely many nonexpansive mappings contractive mapping weakly sequential continuity.
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Finite Dimensional Behavior for Forced Nonlinear Sobolev-Galpern Equations 被引量:1
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作者 Ya-dongShang Bo-lingGuo 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2004年第2期247-256,共10页
This paper deals with the asymptotic behavior of solutions for the nonlinear Sobolev-Galpernequations.We first show the existence of the global weak attractor in H^2(Ω)∩H_0~1(Ω) for the equations.Andthen by an ener... This paper deals with the asymptotic behavior of solutions for the nonlinear Sobolev-Galpernequations.We first show the existence of the global weak attractor in H^2(Ω)∩H_0~1(Ω) for the equations.Andthen by an energy equation we prove that the global weak attractor is actually the global strong attractor.Thefinite-dimensionality of the global attractor is also established. 展开更多
关键词 Nonlinear Sobolev-Galpern equations asymptotic behavior global attractor energy equation weak continuity
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Continuity of Weak Solutions for Quasilinear Parabolic Equations with Strong Degeneracy 被引量:1
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作者 Hongjun YUAN 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2007年第4期475-498,共24页
The aim of this paper is to study the continuity of weak solutions for quasilinear degenerate parabolic equations of the form: μt-△φ(μ) = 0 ,where φ ε C1(R^1) is a strictly monotone increasing function. Cle... The aim of this paper is to study the continuity of weak solutions for quasilinear degenerate parabolic equations of the form: μt-△φ(μ) = 0 ,where φ ε C1(R^1) is a strictly monotone increasing function. Clearly, the above equation has strong degeneracy, i.e., the set of zero points of φ'(.) is permitted to have zero measure. This is an answer to an open problem in [13, p. 288]. 展开更多
关键词 Continuity of weak solutions Quasilinear degenerate parabolic equation
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Weak Continuity and Compactness for Nonlinear Partial Differential Equations
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作者 Gui-Qiang G.CHEN 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2015年第5期715-736,共22页
This paper presents several examples of fundamental problems involving weak continuity and compactness for nonlinear partial differential equations, in which compensated compactness and related ideas have played a sig... This paper presents several examples of fundamental problems involving weak continuity and compactness for nonlinear partial differential equations, in which compensated compactness and related ideas have played a significant role. The compactness and convergence of vanishing viscosity solutions for nonlinear hyperbolic conservation laws are first analyzed, including the inviscid limit from the Navier-Stokes equations to the Euler equations for homentropic flow, the vanishing viscosity method to construct the global spherically symmetric solutions to the multidimensional compressible Euler equations, and the sonic-subsonic limit of solutions of the full Euler equations for multi-dimensional steady compressible fluids. Then the weak continuity and rigidity of the Gauss-Codazzi-Ricci system and corresponding isometric embeddings in differential geometry are revealed. Further references are also provided for some recent developments on the weak continuity and compactness for nonlinear partial differential equations. 展开更多
关键词 Weak continuity Compensated compactness Nonlinear partial differential equations Euler equations Gauss-Codazzi-Ricci system
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Weak Convergence of a Projection Algorithm for Variational Inequalities and Relatively Nonexpansive Mappings in a Banach Space
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作者 Ying LIU 《Journal of Mathematical Research and Exposition》 CSCD 2010年第4期716-724,共9页
In this paper, we introduce an iterative sequence for finding a common element of the set of fixed points of a relatively nonexpansive mapping and the set of solutions of the variational inequality for an inverse-stro... In this paper, we introduce an iterative sequence for finding a common element of the set of fixed points of a relatively nonexpansive mapping and the set of solutions of the variational inequality for an inverse-strongly-monotone mapping in a Banach space. Then we show that the sequence converges weakly to a common element of two sets. 展开更多
关键词 relatively nonexpansive mapping generalized projection inverse-strongly-monotone mapping weakly sequential continuity p-uniformly convexity constant.
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Homogenization of Differential Operators
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作者 Sijue Wu 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2002年第1期9-14,共6页
In this note, we present a method of constructing the homogenized operator for a general sequence of differential operators. As an example, we construct the homogenized operator for a sequence of linear parabolic oper... In this note, we present a method of constructing the homogenized operator for a general sequence of differential operators. As an example, we construct the homogenized operator for a sequence of linear parabolic operators. 展开更多
关键词 HOMOGENIZATION Weak limit Weak continuity of nonlinear operators
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