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A new class of history-dependent quasi variational-hemivariational inequalities with constraints

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arXiv 2023年

作者： Migórski, Stanislaw Bai, Yunru Zeng, Shengda College of Applied Mathematics Chengdu University of Information Technology Sichuan Province Chengdu610225 China School of Science Guangxi University of Science and Technology Guangxi Province Liuzhou545006 China Jagiellonian University in Krakow Faculty of Mathematics and Computer Science ul. Lojasiewicza 6 Krakow30348 Poland Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing Yulin Normal University Guangxi Province Yulin537000 China

In this paper we consider an abstract class of time-dependent quasi variational-hemivariational inequalities which involves history-dependent operators and a set of unilateral constraints. First, we establish the existence and uniqueness of solution by using a recent result for elliptic variational-hemivariational inequalities in reflexive Banach spaces combined with a fixed-point principle for history-dependent operators. Then, we apply the abstract result to show the unique weak solvability to a quasistatic viscoelastic frictional contact problem. The contact law involves a unilateral Signorini-type condition for the normal velocity and the nonmonotone normal damped response condition while the friction condition is a version of the Coulomb law of dry friction in which the friction bound depends on the accumulated *** Codes 35J87, 47J20, 49J40, 49J45, 74G30, 74M15 © 2023, CC BY.

关键词： Friction

On second order differential inclusion driven by quasi-variational–hemivariational inequalities

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Nonlinear Analysis: Real World Applications 2024年 77卷

作者： Liang, Yunshui Ceng, Lu-Chuan Yao, Jen-Chih Zeng, Shengda Department of Mathematics Shanghai Normal University Shanghai200234 China Center for Fundamental Science Kaohsiung Medical University Kaohsiung807 Taiwan Department of Applied Mathematics National Sun Yat-sen University Kaohsiung804 Taiwan Center for Applied Mathematics of Guangxi and Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing Yulin Normal University Guangxi Yulin537000 China Jagiellonian University in Krakow Faculty of Mathematics and Computer Science ul. Lojasiewicza 6 Krakow30-348 Poland

In this paper we investigate an evolution problem (SDQHVI) which constitutes of the second order differential inclusion driven by a quasi-variational–hemivariational inequality (QHVI) with perturbation operator in Banach spaces. Unlike the existing literature on differential inclusions, on the one hand, the second order differential operator is not assumed to be compact;on the other hand, the solvability of the inequality is proved under non-coercive condition. More precisely, first, it is shown that the solution set of the QHVI with perturbation operator is nonempty, bounded, closed and convex under the KKM theorem and the Minty formulation. Then, an associated multivalued map with the solution set of the QHVI with perturbation operator is introduced, and we prove that it is upper semicontinuous and measurable. Finally, by utilizing Kakutani–Fan–Glicksberg fixed point theorem, a weak topology technique and properties of strong continuous cosine operators, we prove the existence of mild solutions for SDQHVI. © 2023 Elsevier Ltd

关键词： Banach spaces

Existence results for variational-hemivariational inequality systems with nonlinear couplings

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arXiv 2022年

作者： Bai, Yunru Costea, Nicuşor Zeng, Shengda School of Science Guangxi University of Science and Technology Guangxi Liuzhou545006 China Department of Mathematics and Computer Science National University of Science and Technology Politehnica Bucharest 313 Splaiul Independent ¸ei Bucharest060042 Romania Guangxi Colleges Universities Key Laboratory of Complex System Optimization and Big Data Processing Yulin Normal University Guangxi Yulin537000 China Jagiellonian University in Krakow Faculty of Mathematics and Computer Science ul. Lojasiewicza 6 Krakow30-348 Poland

MSC Codes 35J88, 39B72, 58E50, 70G75, 74M15In this paper we investigate a system of coupled inequalities consisting of a variational-hemivariational inequality and a quasi-hemivariational inequality on Banach spaces. The approach is topological, and a wide variety of existence results is established for both bounded and unbounded constraint sets in real reflexive Banach spaces. Applications to Contact Mechanics are provided in the last section of the paper. More precisely, we consider a contact model with (possibly) multivalued constitutive law whose variational formulation leads to a coupled system of inequalities. The weak solvability of the problem is proved via employing the theoretical results obtained in the previous section. The novelty of our approach comes from the fact that we consider two potential contact zones and the variational formulation allows us to determine simultaneously the displacement field and the Cauchy stress tensor. © 2022, CC BY.

关键词： Stress tensor

wChain: A fast fault-tolerant blockchain protocol for multihop wireless networks

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arXiv 2021年

作者： Xu, Minghui Liu, Chunchi Zou, Yifei Zhao, Feng Yu, Jiguo Cheng, Xiuzhen Department of Computer Science George Washington University WashingtonDC20052 United States School of Computer Science and Technology Shandong University Qingdao266510 China Guangxi Colleges Universities Key Laboratory of Complex System Optimization and Big Data Processing Yulin Normal University Yulin China Jinan Shandong250353 China Jinan Shandong250014 China Shandong Laboratory of Computer Networks Jinan250014 China

This paper presents wChain, a blockchain protocol specifically designed for multihop wireless networks that deeply integrates wireless communication properties and blockchain technologies under the realistic SINR model. We adopt a hierarchical spanner as the communication backbone to address medium contention and achieve fast data aggregation within O(log N log Γ) slots where N is the network size and Γ refers to the ratio of the maximum distance to the minimum distance between any two nodes. Besides, wChain employs data aggregation and reaggregation, and node recovery mechanisms to ensure efficiency, fault tolerance, persistence, and liveness. The worst-case runtime of wChain is upper bounded by O(f log N log Γ), where f = bN2 c is the upper bound of the number of faulty nodes. To validate our design, we conduct both theoretical analysis and simulation studies, and the results only demonstrate the nice properties of wChain, but also point to a vast new space for the exploration of blockchain protocols in wireless networks. Copyright © 2021, The Authors. All rights reserved.

关键词： Signal interference

A NEW CLASS OF EVOLUTION MULTIVALUED QUASI-VARIATIONAL INEQUALITIES I: EXISTENCE AND NONSMOOTH OPTIMAL CONTROL

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arXiv 2024年

作者： Zeng, Shengda Radulescu, Vicentiu D. Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing Yulin Normal University Guangxi Yulin537000 China Jagiellonian University in Krakow Faculty of Mathematics and Computer Science ul. Lojasiewicza 6 Krakow30-348 Poland Faculty of Applied Mathematics AGH University of Kraków Kraków30-059 Poland Department of Mathematics University of Craiova Craiova200585 Romania Simion Stoilow Institute of Mathematics The Romanian Academy Bucharest010702 Romania

In this paper, we consider a new kind of evolution multivalued quasi-variational inequalities with feedback effect and a nonlinear bifunction which contain several (evolution) quasi-variational/hemivariational inequalities as special cases. The main contribution of this paper is twofold. The first goal is to establish a novel framework for proving the existence of solutions and the compactness of solution set to the evolution multivalued quasi-variational inequalities, under quite mild assumptions. Whereas, the second contribution is to introduce and study a nonlinear and nonsmooth optimal control problem governed by an evolution multivalued quasi-variational inequality, and then to obtain the sufficient conditions for guaranteeing the solvability of the nonlinear and nonsmooth optimal control problem under consideration. Such nonlinear and nonsmooth optimal control problem could as a useful model to explore the simultaneous distributed-boundary optimal control problems driven by evolution multivalued quasi-variational inequalities, and optimal parameters identification for evolution multivalued quasi-variational inequalities. Copyright © 2024, The Authors. All rights reserved.

关键词： Optimal control systems

A Class of Elliptic Quasi–Variational–Hemivariational Inequalities with Applications

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arXiv 2023年

作者： Migórski, Stanislaw Yao, Jen-Chih Zeng, Shengda College of Applied Mathematics Chengdu University of Information Technology Sichuan Province Chengdu610225 China Jagiellonian University in Krakow Chair of Optimization and Control ul. Lojasiewicza 6 Krakow30348 Poland Center for General Education China Medical University Taichung Taiwan Guangxi Colleges Universities Key Laboratory of Complex System Optimization and Big Data Processing Yulin Normal University Guangxi Yulin537000 China Jagiellonian University in Krakow Faculty of Mathematics and Computer Science ul. Lojasiewicza 6 Krakow30348 Poland

equalities in reflexive Banach spaces. The inequalities contain a convex potential, a locally Lipschitz superpotential, and a solution-dependent set of constraints. Solution existence and compactness of the solution set to the inequality problem are established based on the Kakutani–Ky Fan–Glicksberg fixed point theorem. Two examples of the interior and boundary semipermeability models illustrate the applicability of our *** Codes 35L15, 35L86, 35L87 © 2023, CC BY.

关键词： Banach spaces

A Distributed Dynamic Adaptive and Fast Balancing SDN Controller Management

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IOP Conference Series: Earth and Environmental Science 2019年第1期234卷

作者： Yang Liu Qian He Xiongying Li Shuiming Zhou Guangxi Transportation Research and Consulting Co. Ltd Nanning 530007 China Guangxi Key Laboratory of Cryptograph and Information Security Guangxi University Key Laboratory of Cloud Computing and Complex System Guilin University of Electronic Technology Guilin 541004 China

Tradition Software Defined Network (SDN) suffers from single point failure and uneven load distribution problems. Multiple SDN controllers work together to construct a distributed dynamic adaptive cluster with dynamic load balancing for large scale SDN switch stream requesting. Introducing such features as CPU, memory and network load, a Dynamic Adaptive and Fast algorithm (DAF) can select source, target and destination SDN controllers to balance load dynamically. The results of experiments show that DAF works well and improve the cloud service system throughput.

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DOUBLE PHASE IMPLICIT OBSTACLE PROBLEMS WITH CONVECTION AND MULTIVALUED MIXED BOUNDARY VALUE CONDITIONS

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arXiv 2021年

作者： Zeng, Shengda Rǎdulescu, Vicenţiu D. Winkert, Patrick Guangxi Colleges Universities Key Laboratory of Complex System Optimization and Big Data Processing Yulin Normal University Guangxi Yulin537000 China Jagiellonian University in Krakow Faculty of Mathematics and Computer Science ul. Lojasiewicza 6 Krakow30-348 Poland Faculty of Applied Mathematics Agh University of Science and Technology Kraków30-059 Poland Department of Mathematics University of Craiova Craiova200585 Romania Technische Universität Berlin Institut für Mathematik Straße des 17. Juni 136 Berlin10623 Germany

In this paper we consider a mixed boundary value problem with a nonhomogeneous, nonlinear differential operator (called double phase operator), a nonlinear convection term (a reaction term depending on the gradient), three multivalued terms and an implicit obstacle constraint. Under very general assumptions on the data, we prove that the solution set of such implicit obstacle problem is nonempty (so there is at least one solution) and weakly compact. The proof of our main result uses the Kakutani-Ky Fan fixed point theorem for multivalued operators along with the theory of nonsmooth analysis and variational methods for pseudomonotone operators. Copyright © 2021, The Authors. All rights reserved.

关键词： Fixed point arithmetic

Fuzzy Stability of the Orthogonal Cauchy Functional equations

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Chinese Quarterly Journal of Mathematics 2018年第3期33卷 302-312页

作者： BI Lv-qing DAI Song-song HU BO School of Electronics and Communication Engineering Guangxi Colleges and Universities KeyLaboratory of Complex System Optimization and Big Data Processing Yulin Normal UniversityYulin537000P.R.China. School of Information Science and Engineering Xiamen UniversityXiamen 361005P.R.China. School of Mechanical and Electrical Engineering Guizhou Normal UniversityGuiyang 550025P.R.China.

In this paper, we establish fuzzy stability of the orthogonal Cauchy functional equations f(x + y) = f(x) + f(y), x ⊥ y and the orthogonal Cauchy functional of P exider type f(x + y) = g(x) + h(y), x ⊥ y in which ⊥... 详细信息

关键词： Fuzzy normed space Hyers-Ulam stability Orthogonally Cauchy functionalequation Orthogonally Cauchy functional Pexider equation Orthogonality space