关键词：
3D Navier-Stokes-Voigt equations;admissible trajectories set;admissible control set;feedback control;time optimal control
摘要：
In this article, we discuss a time optimal feedback control for asymmetrical 3D Navier–Stokes–Voigt equations. Firstly, we consider the existence of the admissible trajectories for the asymmetrical 3D Navier–Stokes–Voigt equations by using the well-known Cesari property and the Fillippove’s theorem. Secondly, we study the existence result of a time optimal control for the feedback control systems. Lastly, asymmetrical Clarke’s subdifferential inclusions and asymmetrical 3D Navier–Stokes–Voigt differential variational inequalities are given to explain our main results.
期刊：
JOURNAL OF APPLIED ANALYSIS AND COMPUTATION,2022年12(4):1308-1327 ISSN：2156-907X
通讯作者：
Bin, M.
作者机构：
[Shi, Cuiyun] Guilin Univ Technol Nanning, Sch Basic Sci, Nanning 530001, Guangxi Provinc, Peoples R China.;[Li, Yunxiang; Bin, Maojun] Yulin Normal Univ, Guangxi Coll & Univ, Key Lab Complex Syst Optimizat & Big Data Proc, Yulin 537000, Guangxi Provinc, Peoples R China.;[Li, Yunxiang] Hunan City Univ, Coll Sci, Yiyang 413000, Hunan, Peoples R China.
通讯机构：
Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing, Yulin Normal University, Guangxi Province, Yulin, China
摘要：
In this paper, we discuss a class of Caputo fractional evolution equations on Banach space with feedback control constraint whose value is non-convex closed in the control space. First, we prove the existence of solutions for the system with feedback control whose values are the extreme points of the convexified constraint that belongs to the original one. Secondly, we study the topological properties of the sets of admissible “state-control” pair for the original system with various feedback control constraints and the relations between them. Moreover, we obtain necessary and sufficient conditions for the solution set of original systems to be closed. In the end, an example is given to illustrate the applications of our main results.
摘要：
We consider a mathematical model which describes the frictional contact between a deformable body and a foundation. The process is assumed to be quasistatic and the material behaviour is described by a viscoelastic constitutive law with damage. The friction and contact are modeled with subdifferential boundary conditions. We derive the variational formulation of the problem which is a coupled system of a hemivariational inequality for the velocity and a parabolic variational inequality for the damage field. Then we prove the existence of a unique weak solution to the model. The proof is based on arguments of time-dependent stationary inclusions and a fixed point theorem.
期刊：
Journal of Mathematical Analysis and Applications,2015年427(2):646-668 ISSN：0022-247X
通讯作者：
Han, Jiangfeng
作者机构：
[Han, Jiangfeng; Migorski, Stanislaw] Jagiellonian Univ, Inst Comp Sci, Fac Math & Comp Sci, PL-30348 Krakow, Poland.;[Li, Yunxiang] Hunan City Univ, Dept Math, Yiyang 413000, Hunan, Peoples R China.;[Han, Jiangfeng] Jagiellonian Univ, Inst Comp Sci, Fac Math & Comp Sci, Ul Lojasiewicza 6, PL-30348 Krakow, Poland.
通讯机构：
[Han, Jiangfeng] J;Jagiellonian Univ, Inst Comp Sci, Fac Math & Comp Sci, Ul Lojasiewicza 6, PL-30348 Krakow, Poland.
关键词：
Variational-hemivariational inequality;Clarke subdifferential;Existence and uniqueness;Viscoelastic materials;Quasistatic;Fixed point theorem
摘要：
The goal of this paper is to study a mathematical model which describes the adhesive contact between a deformable body and a foundation. The body consists of a viscoelastic material with long memory and the process is assumed to be quasistatic. The adhesive contact condition on the normal plane is modeled by a version of normal compliance condition with unilateral constraint in which adhesion is taken into account, the adhesive contact condition on the tangential plane is described by an adhesive Clarke subdifferential condition, and the evolution of the bonding field is described by an ordinary differential equation. We derive the variational formulation of this problem which is a system of a variational-hemivariational inequality for the displacement field and an ordinary differential equation for the bonding field. Then, we obtain existence and uniqueness results on abstract inclusions and abstract variational-hemivariational inequalities. Finally, we apply the abstract results to prove the existence of a unique weak solution to the contact problem. (C) 2015 Elsevier Inc. All rights reserved.
摘要：
In this paper, we deal with a class of inequality problems for dynamic frictional contact between a piezoelectric body and a foundation. The model consists of a system of the hemivariational inequality of hyperbolic type for the displacement, the time dependent elliptic equation for the electric potential. The contact is modeled by a general normal damped response condition and a friction law, which are nonmonotone, possibly multivalued and have the subdifferential form. The existence of a weak solution to the model is proved by embedding the problem into a class of second-order evolution inclusions and by applying a surjectivity result for multivalued operators.
