A sufficient condition for the Mosco limit of a sequence of quasi-regular Dirichlet forms to be quasi-regular is given. In particular, a Dirichlet form is a quasi-regular Dirchlet form if and only if its Yosida approx...A sufficient condition for the Mosco limit of a sequence of quasi-regular Dirichlet forms to be quasi-regular is given. In particular, a Dirichlet form is a quasi-regular Dirchlet form if and only if its Yosida approximation sequency satisfies the conditon. Furthermore, conditions for the Mosco limit of a sequence of symmetric (strictly strong) local quasi-regular Dirichlet forms to be (strictly strong) local are also presented. This paper extends the results of [1] from regular Dirichlet space to quasi-regular Dirichlet space.展开更多
We consider a differential variational-hemivariational inequality with constraints,in the framework of reflexive Banach spaces.The existence of a unique mild solution of the inequality,together with its stability,was ...We consider a differential variational-hemivariational inequality with constraints,in the framework of reflexive Banach spaces.The existence of a unique mild solution of the inequality,together with its stability,was proved in[1].Here,we complete these results with existence,uniqueness and convergence results for an associated penalty-type method.To this end,we construct a sequence of perturbed differential variational-hemivariational inequalities governed by perturbed sets of constraints and penalty coefficients.We prove the unique solvability of each perturbed inequality as well as the convergence of its solution to the solution of the original inequality.Then,we consider a mathematical model which describes the equilibrium of a viscoelastic rod in unilateral contact.The weak formulation of the model is in a form of a differential variational-hemivariational inequality in which the unknowns are the displacement field and the history of the deformation.We apply our abstract penalty method in the study of this inequality and provide the corresponding mechanical interpretations.展开更多
In this paper,we provide the stability analysis for an evolutionary variational-hemivariational inequality in the reflexive Banach space,whose data including the constraint set are perturbed.First,by using its perturb...In this paper,we provide the stability analysis for an evolutionary variational-hemivariational inequality in the reflexive Banach space,whose data including the constraint set are perturbed.First,by using its perturbed data and the duality mapping,the perturbed and regularized problems for the evolutionary variational-hemivariational inequality are constructed,respectively.Then,by proving the unique solvability for the evolutionary variational-hemivariational inequality and its perturbed and regularized problems,we obtain two sequences called approximating sequences of the solution to the evolutionary variational-hemivariational inequality,and prove their strong convergence to the unique solution to the evolutionary variationalhemivariational inequality under different mild conditions.展开更多
Weak convergence of Markov processes is studied by means of Dirichlet forms and two theorems for weak convergence of Hunt processes on general metric spaces are established. As applications, examples for weak converge...Weak convergence of Markov processes is studied by means of Dirichlet forms and two theorems for weak convergence of Hunt processes on general metric spaces are established. As applications, examples for weak convergence of symmetric or non symmetric Dirichlet processes on finite and infinite spaces are given.展开更多
The notions of fuzzy (super) pramart are introduced. Then the completeness and separability of metric space are discussed. A necessary and sufficient condition of convergence for fuzzy sequences is provided. Finally, ...The notions of fuzzy (super) pramart are introduced. Then the completeness and separability of metric space are discussed. A necessary and sufficient condition of convergence for fuzzy sequences is provided. Finally, the graph Kuratowski-Mosco convergence and D-convergence of fuzzy (super) pramart and quasi-martingale are studied.展开更多
文摘A sufficient condition for the Mosco limit of a sequence of quasi-regular Dirichlet forms to be quasi-regular is given. In particular, a Dirichlet form is a quasi-regular Dirchlet form if and only if its Yosida approximation sequency satisfies the conditon. Furthermore, conditions for the Mosco limit of a sequence of symmetric (strictly strong) local quasi-regular Dirichlet forms to be (strictly strong) local are also presented. This paper extends the results of [1] from regular Dirichlet space to quasi-regular Dirichlet space.
基金supported by the European Union’s Horizon 2020 Research and Innovation Programme under the Marie Sklodowska-Curie Grant Agreement(823731CONMECH)supported by National Natural Science Foundation of China(11671101),supported by National Natural Science Foundation of China(11961074)+2 种基金Guangxi Natural Science Foundation(2021GXNSFAA075022)Project of Guangxi Education Department(2020KY16017)Yulin normal university of scientific research fund for high-level talents(G2019ZK39,G2021ZK06)。
文摘We consider a differential variational-hemivariational inequality with constraints,in the framework of reflexive Banach spaces.The existence of a unique mild solution of the inequality,together with its stability,was proved in[1].Here,we complete these results with existence,uniqueness and convergence results for an associated penalty-type method.To this end,we construct a sequence of perturbed differential variational-hemivariational inequalities governed by perturbed sets of constraints and penalty coefficients.We prove the unique solvability of each perturbed inequality as well as the convergence of its solution to the solution of the original inequality.Then,we consider a mathematical model which describes the equilibrium of a viscoelastic rod in unilateral contact.The weak formulation of the model is in a form of a differential variational-hemivariational inequality in which the unknowns are the displacement field and the history of the deformation.We apply our abstract penalty method in the study of this inequality and provide the corresponding mechanical interpretations.
基金supported by National Natural Science Foundation of China(Grant Nos.11771067 and 11671282)the Applied Basic Project of Sichuan Province(Grant No.2019YJ0204)the Fundamental Research Funds for the Central Universities(Grant No.ZYGX2019J095)。
文摘In this paper,we provide the stability analysis for an evolutionary variational-hemivariational inequality in the reflexive Banach space,whose data including the constraint set are perturbed.First,by using its perturbed data and the duality mapping,the perturbed and regularized problems for the evolutionary variational-hemivariational inequality are constructed,respectively.Then,by proving the unique solvability for the evolutionary variational-hemivariational inequality and its perturbed and regularized problems,we obtain two sequences called approximating sequences of the solution to the evolutionary variational-hemivariational inequality,and prove their strong convergence to the unique solution to the evolutionary variationalhemivariational inequality under different mild conditions.
基金Project partially supported by the National Natural Science Foundation of ChinaTianyuan Mathematics Foundation.
文摘Weak convergence of Markov processes is studied by means of Dirichlet forms and two theorems for weak convergence of Hunt processes on general metric spaces are established. As applications, examples for weak convergence of symmetric or non symmetric Dirichlet processes on finite and infinite spaces are given.
基金the Key Project of the Ministry of Education of China (205073)Research Fund for Doctorial Program of Higher Education (No.20060255006)
文摘The notions of fuzzy (super) pramart are introduced. Then the completeness and separability of metric space are discussed. A necessary and sufficient condition of convergence for fuzzy sequences is provided. Finally, the graph Kuratowski-Mosco convergence and D-convergence of fuzzy (super) pramart and quasi-martingale are studied.
