Convergence analysis on Browder-Tikhonov regularization for second-order evolution hemivariational inequality

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.

Evolution Hemivariational Inequality with Hysteresis Operator in Higher Order Term

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.

ANALYSIS OF AN ELASTO-PIEZOELECTRIC SYSTEM OF HEMIVARIATIONAL INEQUALITIES WITH THERMAL EFFECTS

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.

SEMILINEAR HEMIVARIATIONAL INEQUALITIES WITH STRONG RESONANCE AT INFINITY

A semilinear elliptic equation with strong resonance at infinity and with a nonsmooth potential is studied. Using nonsmooth critical point theory and developing some abstract minimax principles which complement and extend results in the literature, two results on existence are obtained.

INVERSE COEFFICIENT PROBLEMS FOR PARABOLIC HEMIVARIATIONAL INEQUALITIES

This paper is devoted to the class of inverse problems for a nonlinear parabolic hemivariational inequality. The unknown coefficient of the operator depends on the gradient of the solution and belongs to a set of admissible coefficients. It is proved that the convergence of solutions for the corresponding direct problems continuously depends on the coefficient convergence. Based on this result the existence of a quasisolution of the inverse problem is obtained.

ON QUASILINEAR ELLIPTIC HEMIVARIATIONAL INEQUALITIES

lit the present paper, quasilinear elliptic hemivariational inequalities as a generalization to nonconvex functionals of the elliptic variational inequalities are studied. This extension is strongly motivated by various problems in mechanics. By using the notion of the generalized gradient of Clarke and the theory of pseudomonotone operators, the existence of solutions is proved.

A CLASS OF PARABOLIC HEMIVARIATIONAL INEQUALITIES

Quasilinear parabolic hemivariational inequalities as a generalization to nonconvex functions of the parabolic variational inequalities are discussed. This extension is strongly motivated by various problems in mechanics. By use of the notion of the generalized gradient of Clarke and the theory of pseudomonotone operators, it is proved there exists at least one solution.

Differential Evolution Hemivariational Inequalities with Anti-periodic Conditions

The goal of this paper is to deal with a new dynamic system called a differential evolution hemivariational inequality(DEHVI)which couples an abstract parabolic evolution hemivariational inequality and a nonlinear differential equation in a Banach space.First,by apply ing surjectivity result for pseudomonotone multivalued mappins and the properties of Clarke's subgradient,we show the nonempty of the solution set for the parabolic hemivariational inequality.Then,some topological properties of the solution set are established such as boundedness,closedness and convexity.Furthermore,we explore the upper semicontinuity of the solution mapping.Finally,we prove the solution set of the system(DEHVI)is nonempty and the set of all trajectories of(DEHVI)is weakly compact in C(I,X).

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

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 law.First,a variational formulation of the model is obtained;that is a nonlinear boundary hemivariational inequality of parabolic type for the velocity field.Then,an abstract first-order evolutionary hemivariational inequality in the framework of an evolution triple of spaces is investigated.Under mild assumptions,the nonemptiness and weak compactness of the set of periodic solutions to the abstract inequality are proven.Furthermore,a uniqueness theorem for the abstract inequality is established by using a monotonicity argument.Finally,we employ the theoretical results to examine the nonstationary Oseen model.

MULTIVALUED DIFFERENTIAL EQUATIONS IN BANACH SPACES AND THEIR APPLICATIONS

This paper studies the existence of solutions to a class of multivalued differential equations by using a surjectivity result for multivalued (S+) type mappings. The authors then apply their results to evolution hemivariational inequalities and parabolic equations with nonmonotone discontinuities, which generalize and extend previously known theorems.

ANTI-PERIODIC SOLUTIONS FOR DIFFERENTIAL INCLUSIONS IN BANACH SPACES AND THEIR APPLICATIONS

We deal with anti-periodic problems for differential inclusions with nonmonotone perturbations. The main tools in our study are the maximal monotone property of the derivative operator with anti-periodic conditions and the theory of pseudomonotone perturbations of maximal monotone mappings. We then apply our results to evolution hemivariational inequalities and parabolic equations with nonmonotone discontinuities, which generalize and extend previously known theorems.

Existence of anti-periodic solutions for hemivariational inequalities

J.Y. Park and T. G. Ha [Nonlinear Anal., 2008, 68： 747-767; 2009, 7h 3203-3217] investigated the existence of anti-periodic solutions for hemivariational inequalities with a pseudomonotone operator. In this note, we point out that the methods used there are not suitable for the proof of the existence of anti-periodic solutions for hemivariational inequalities and we shall give a straightforward approach to handle these problems. The main tools in our study are the maximal monotone property of the derivative operator with anti- periodic conditions and the surjectivity result for L-pseudomonotone operators.

Inverse Coefficient Problems for Elliptic Hemivariational Inequalities

This paper is devoted to a class of inverse coefficient problems for nonlinear elliptic hemivariational inequalities. The unknown coefficient of elliptic hemivariational inequalities depends on the gradient of the solution and belongs to a set of admissible coefficients. It is shown that the nonlinear elliptic hemivariational inequalities are uniquely solvable for the given class of coefficients. The result of existence of quasisolutions of the inverse problems is obtained.

A CLASS OF QUASILINEAR ELLIPTIC HEMIVARIATIONAL INEQUALITIES

In this paper, we shall deal with quasilinear elliptic hemivariational inequalities. By the use of the theory of multivalued pseudomonotone mappings, we will prove the existence of solutions.