This paper studies the Browder-Tikhonov regularization of a second-order evolution hemivariational inequality （SOEHVI） with non-coercive operators. With duality mapping, the regularized formulations and a derived fi...This paper studies the Browder-Tikhonov regularization of a second-order evolution hemivariational inequality （SOEHVI） with non-coercive operators. With duality mapping, the regularized formulations and a derived first-order evolution hemivariational inequality （FOEHVI） for the problem considered are presented. By applying the Browder-Tikhonov regularization method to the derived FOEHVI, a sequence of regularized solutions to the regularized SOEHVI is constructed, and the strong convergence of the whole sequence of regularized solutions to a solution to the problem is proved.展开更多
A dynamic contact problem for elastic-viscoplastic materials with thermal effects is investigated. The contact is bilateral, and the friction is modeled with Tresca＇s friction law with heat exchange. A variational fo...A dynamic contact problem for elastic-viscoplastic materials with thermal effects is investigated. The contact is bilateral, and the friction is modeled with Tresca＇s friction law with heat exchange. A variational formulation of the model is derived, and the existence of a unique weak solution is proved. The proofs are based on the classical result of nonlinear first order evolution inequalities, the equations with monotone operators, and the fixed point arguments. Finally, the continuous dependence of the solution on the friction yield limit is studied.展开更多
In this paper we prove the existence and uniqueness of a weak solution for a dynamic electo-viscoetastic problem that describes a contact between a body and a foundation. We assume the body is made from thermoviscoela...In this paper we prove the existence and uniqueness of a weak solution for a dynamic electo-viscoetastic problem that describes a contact between a body and a foundation. We assume the body is made from thermoviscoelastic material and consider nonmonotone boundary conditions for the contact. We use recent results from the theory of hemivariational inequalities and the fixed point theory.展开更多
The authors study evolution hemivariational inequalities of semilinear type containing a hysteresis operator. For such problems we establish an existence result by reducing the order of the equation and then by the us...The authors study evolution hemivariational inequalities of semilinear type containing a hysteresis operator. For such problems we establish an existence result by reducing the order of the equation and then by the use of the time-discretization procedure.展开更多
In this parer, by using the polar coordinates for the generalized Baouendi- Grushin operatorLα=∑i=1^n 偏d^2/偏dxi^2＋∑j=1^m｜x｜^2α偏d^2/偏dy^2j,where x = （x1,x2,……,Xn）∈R^n,y = （y1,y2,… ,ym） ∈,α 〉 0, we...In this parer, by using the polar coordinates for the generalized Baouendi- Grushin operatorLα=∑i=1^n 偏d^2/偏dxi^2＋∑j=1^m｜x｜^2α偏d^2/偏dy^2j,where x = （x1,x2,……,Xn）∈R^n,y = （y1,y2,… ,ym） ∈,α 〉 0, we obtain the volume of the ball associated to Lα and prove the nonexistence for a second order evolution inequality which is relative to Lα.展开更多
基金supported by the National Natural Science Foundation of China(Nos.11101069,11171237,11471059,and 81171411)the China Postdoctoral Science Foundation(Nos.2014M552328 and2015T80967)the Scientific Research Foundation for the Returned Overseas Chinese Scholars,State Education Ministry
文摘This paper studies the Browder-Tikhonov regularization of a second-order evolution hemivariational inequality （SOEHVI） with non-coercive operators. With duality mapping, the regularized formulations and a derived first-order evolution hemivariational inequality （FOEHVI） for the problem considered are presented. By applying the Browder-Tikhonov regularization method to the derived FOEHVI, a sequence of regularized solutions to the regularized SOEHVI is constructed, and the strong convergence of the whole sequence of regularized solutions to a solution to the problem is proved.
文摘A dynamic contact problem for elastic-viscoplastic materials with thermal effects is investigated. The contact is bilateral, and the friction is modeled with Tresca＇s friction law with heat exchange. A variational formulation of the model is derived, and the existence of a unique weak solution is proved. The proofs are based on the classical result of nonlinear first order evolution inequalities, the equations with monotone operators, and the fixed point arguments. Finally, the continuous dependence of the solution on the friction yield limit is studied.
基金supported by the Marie Curie International Research Staff Exchange Scheme Fellowship within the 7th European Community Framework Programme under Grant Agreement No.295118the National Science Center of Poland under the Maestro Advanced Project No.DEC-2012/06/A/ST1/00262
文摘In this paper we prove the existence and uniqueness of a weak solution for a dynamic electo-viscoetastic problem that describes a contact between a body and a foundation. We assume the body is made from thermoviscoelastic material and consider nonmonotone boundary conditions for the contact. We use recent results from the theory of hemivariational inequalities and the fixed point theory.
文摘The authors study evolution hemivariational inequalities of semilinear type containing a hysteresis operator. For such problems we establish an existence result by reducing the order of the equation and then by the use of the time-discretization procedure.
文摘In this parer, by using the polar coordinates for the generalized Baouendi- Grushin operatorLα=∑i=1^n 偏d^2/偏dxi^2＋∑j=1^m｜x｜^2α偏d^2/偏dy^2j,where x = （x1,x2,……,Xn）∈R^n,y = （y1,y2,… ,ym） ∈,α 〉 0, we obtain the volume of the ball associated to Lα and prove the nonexistence for a second order evolution inequality which is relative to Lα.
