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TIME PERIODIC SOLUTIONS TO THE EVOLUTIONARY OSEEN MODEL FOR A GENERALIZED NEWTONIAN INCOMPRESSIBLE FLUID

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Acta Mathematica Scientia 2023年第4期43卷 1645-1667页

作者：岑金夏 stanislaw migórski Emilio VILCHES 曾生达 School of Mathematical Sciences Zhejiang Normal UniversityJinhua 321004China Jagiellonian University in Krakow Chair of Optimization and Controlul.Lojasiewicza 630348 KrakowPoland Instituto de Ciencias de la Ingenier´ıa Universidad de O’HigginsAv.Libertador Bernardo OHiggins 6112841959 RancaguaChile Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing Yulin Normal UniversityYulin 537000China Department of Mathematics Nanjing University Nanjing 210093China Jagiellonian University in Krakow Faculty of Mathematics and Computer Scienceul.Lojasiewicza 630348 KrakowPoland

In this paper we study a nonstationary Oseen model for a generalized Newtonian incompressible fluid with a time periodic condition and a multivalued,nonmonotone friction ***,a variational formulation of the model is obtained;that is a nonlinear boundary hemivariational inequality of parabolic type for the velocity ***,an abstract first-order evolutionary hemivariational inequality in the framework of an evolution triple of spaces is *** mild assumptions,the nonemptiness and weak compactness of the set of periodic solutions to the abstract inequality are ***,a uniqueness theorem for the abstract inequality is established by using a monotonicity ***,we employ the theoretical results to examine the nonstationary Oseen model.

关键词： nonstationary Oseen model Newtonian incompressible fluid hemivariational inequality periodic solution generalized subgradient

A new class of generalized quasi-variational inequalities with applications to Oseen problems under nonsmooth boundary conditions

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Science China Mathematics 2024年第2期67卷 315-338页

作者： Shengda Zeng Akhtar A.Khan stanislaw migórski Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing Yulin Normal UniversityYulin 537000China Faculty of Mathematics and Computer Science Jagiellonian University in Krak´owKrak´ow 30348Poland Center for Applied and Computational Mathematics School of Mathematical SciencesRochester Institute of TechnologyRochesterNY 14623USA College of Sciences Beibu Gulf UniversityQinzhou 535000China

In this paper, we study a generalized quasi-variational inequality (GQVI for short) with twomultivalued operators and two bifunctions in a Banach space setting. A coupling of the Tychonov fixedpoint principle and the Katutani-Ky Fan theorem for multivalued maps is employed to prove a new existencetheorem for the GQVI. We also study a nonlinear optimal control problem driven by the GQVI and givesufficient conditions ensuring the existence of an optimal control. Finally, we illustrate the applicability of thetheoretical results in the study of a complicated Oseen problem for non-Newtonian fluids with a nonmonotone andmultivalued slip boundary condition (i.e., a generalized friction constitutive law), a generalized leak boundarycondition, a unilateral contact condition of Signorini’s type and an implicit obstacle effect, in which themultivalued slip boundary condition is described by the generalized Clarke subgradient, and the leak boundarycondition is formulated by the convex subdifferential operator for a convex superpotential.

关键词： generalized quasi-variational inequality existence theorem optimal control Kakutani-Ky Fan theorem Oseen problem non-Newtonian fluid nonmonotone slip boundary condition

Optimal control of differential quasivariational-hemivariational inequalities with applications

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Science China Mathematics 2024年第11期67卷 2587-2606页

作者： Dong-ling Cai stanislaw migórski Yi-bin Xiao School of Mathematical Sciences University of Electronic Science and Technology of ChinaChengdu 611731China College of Applied Mathematics Chengdu University of Information TechnologyChengdu 610225China Chair of Optimization and Control Jagiellonian University in KrakowKrakow 30348Poland

In this paper,we study a new class of differential quasivariational-hemivariational inequalities of the elliptic *** problem consists of a system coupling the Cauchy problem for an ordinary differential equation with the variational-hemivariational inequalities,unilateral constraints,and history-dependent ***,based on the Minty formulation and the continuity of the solution map of a parametrized quasivariational-hemivariational inequality,and a fixed point theorem for a history-dependent operator,we prove a result on the ***,we examine optimal control problems for differential quasivariational-hemivariational inequalities,including a time-optimal control problem and a maximum stay control problem,for which we show the existence of *** all the optimal control problems,the system is controlled through a distributed and boundary control,a control in initial conditions,and a control that appears in history-dependent ***,we illustrate the results by considering a nonlinear controlled system for a time-dependent elliptic equation with unilateral constraints.

关键词： differential variational-hemivariational inequality unilateral constraint history-dependent operator optimal control time-optimal control maximum stay problem

EXISTENCE AND CONVERGENCE RESULTS FOR AN ELASTIC FRICTIONAL CONTACT PROBLEM WITH NONMONOTONE SUBDIFFERENTIAL BOUNDARY CONDITIONS

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Acta Mathematica Scientia 2021年第4期41卷 1151-1168页

作者： Yongjian LIU Stanisiaw migÓrski Van Thien NGUYEN Shengda ZHENG Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing Yulin Normal UniversityYulin 537000China College of Applied Mathematics Chengdu University of Information TechnologyChengdu 610225China Jagiellonian University in Krakow Chair of Optimization and Controlul.Lojasiewicza 630348 KrakowPoland Departement of Mathematics FPT UniversityEducation ZoneHoa Lac High Tech ParkKm29 Thang Long HighwayThach That WardHanoiVietnam

The goal of this paper is to study a mathematical model of a nonlinear static frictional contact problem in elasticity with the mixed boundary conditions described by a combination of the Signorini unilateral frictionless contact condition,and nonmonotone multivalued contact,and friction laws of subdifferential ***,under suitable assumptions,we deliver the weak formulation of the contact model,which is an elliptic system with Lagrange multipliers,and which consists of a hemivariational inequality and a variational ***,we prove the solvability of the contact ***,employing the notion of H-convergence of nonlinear elasticity tensors,we provide a result on the convergence of solutions under perturbations which appear in the elasticity operator,body forces,and surface tractions.

关键词： Mixed variational-hemi variational inequality H-convergence homogenization Clarke subgradient Lagrange multiplier elasticity operator

由拟线性反应扩散方程所驱动的非静态不可压缩Navier-Stokes系统

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Science China Mathematics 2021年

作者：曾生达 stanislaw migórski 刘振海玉林师范学院数学与统计学院广西高校复杂系统优化与大数据处理重点实验室 Faculty of Mathematics and Computer Science Jagiellonian University in Krakow 广西民族大学数学与物理学院

本文考虑一类由非单调多值边界条件的非静态不可压缩Navier-Stokes方程和Neumann边界条件的广义拟线性反应扩散方程所构成的新动力系统,该系统可形式化为非线性抛物方程和发展型H半变分不等式所组成的耦合系统.为获得全局弱解存在性,首... 详细信息

本文考虑一类由非单调多值边界条件的非静态不可压缩Navier-Stokes方程和Neumann边界条件的广义拟线性反应扩散方程所构成的新动力系统,该系统可形式化为非线性抛物方程和发展型H半变分不等式所组成的耦合系统.为获得全局弱解存在性,首先,运用后向Euler法与反馈迭代技术引进耦合系统的时间半离散逼近问题;而后,沿用弱-弱上半连续集值算子的满射定理证明逼近问题解的存在性和先验估计;最后,采用极限过程建立系统全局弱解的存在性定理.

关键词：非静态不可压缩Navier-Stokes方程 H半变分不等式 Clarke次梯度半群反应扩散方程半离散逼近系统满射性

Gas-dynamic phenomena caused by rock mass tremors and rock bursts

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International Journal of Mining Science and Technology 2020年第3期30卷 413-420页

作者： stanislaw Wasilewski The Strata Mechanics Research Institute of the Polish Academy of Science ul.Reymonta 2730-059 KrakowPoland

Similar to coal, rock and gas ejections, rock mass tremors and rock bursts are among the most serious natural hazards accompanying the underground extraction of coal. Gas-dynamic phenomena caused by rock mass tremors and rock bursts observed as transient states of air parameters in mining headings,are usually generated as a result of a change in the geometry of headings and the release of considerable amounts of gases. Particular significance is attributed to transient states caused by disasters, which are often accompanied by rapid incidents, presenting threats to the life and health of the underground *** Polish mining there are known examples of transient states of air parameters recorded during gasdynamic phenomena, e.g. tremors and rock bursts. The paper presents the case studies of rapid seismic incidents to show how records in mine monitoring systems broaden the knowledge about the transient states of air parameters in mining headings generated because of them.

关键词： Rock mass tremors Rock bursts Gas-dynamic phenomena Transient states of air parameters Mine monitoring systems

Uncertainty in public health models treated by differential inclusions

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International Journal of Modeling, Simulation, and Scientific Computing 2020年第4期11卷 224-236页

作者： stanislaw Raczynski Faculty of Engineering Universidad Panamericana Augusto Rodin No.49803920 Mexico CityD.F.Mexico

An application of differential inclusions in the epidemic spread models is *** mostly used epidemic models are discussed here,and a brief survey of epidemic modeling is *** of the models are some modifications of the Susceptible–Infected–Recovered *** simulations are carried ***,we consider the influence of some uncertain *** is pointed out that the presence of some fluctuating model parameters can be treated by differential *** solution to such differential inclusion is given in the form of reachable sets for model ***,we focus on the differential inclusion application rather than the model construction.

关键词： Modeling simulation epidemics public health sensitivity differential inclusions.

Simulation and optimization in marketing:Optimal control of consumer goodwill,price and investment

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International Journal of Modeling, Simulation, and Scientific Computing 2014年第3期5卷 33-47页

作者： stanislaw Raczynski Universidad Panamerciana Faculty of Engineering 498 Augusto Rodin03920 Mexico CityMexico

Dynamic market optimization with respect to price,advertisement and investment is *** market model is *** main parameters are the elasticities with respect to price,advertisement and consumer *** elements has been added to the static model based on the market *** parameters like seasonal index and consumer income are functions of time,and the whole market can grow due to the *** tools of the optimal control theory are applied to calculate optimal policy for product price,advertisement and investment,controlled *** total revenue at the end of a fixed time interval is maximized.

关键词： Marketing optimization modeling simulation

Simultaneous events, singularity in the space of models and chicken game

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International Journal of Modeling, Simulation, and Scientific Computing 2021年第4期12卷 1-11页

作者： stanislaw Raczynski Facultad de Ingenier´ıa Universidad Panamericana Augusto Rodin 498Ciudad de M´exico 03920M´exico

The discrete event simulation with simultaneous events is *** models are treated as some points in the general space of *** main topic of this paper is the convergence of sequences of continuous models to the corresponding discrete event *** is pointed out that the discrete event models may represent some singularities in the space of *** fact is related to the problem of validity of discrete event *** models presented here are not the topic of the *** are known models,used as *** model of the“chicken game”and multiple elastic collisions are *** is shown that if a discrete event model is some special limit case of a sequence of continuous models with finite event duration,then that limit model is a *** may provide results very different from the expected limit value of the results from the converging sequence of models.

关键词： Simulation discrete events modeling