HYPERBOLIC HEMIVARIATIONAL INEQUALITIES WITH BOUNDARY SOURCE AND DAMPING TERMS

Hardy Inequalities with Boundary Terms

In this note, we present some Hardy type inequalities for functions which do not vanish on the boundary of a given domain. We establish these inequalities for both bounded and unbounded domains and also obtain the best embedding constants in these inequalities for special domains. Our results are motivated by and building upon some recent work in [5, 6, 9, 12].

Optimal Control Problems for Parabolic Hemivariational Inequalities with Boundary Conditions

In this paper, we study optimal control problems for parabolic hemivariational inequalities of dynamic elasticity and investigate the continuity of the solution mapping from the given initial value and control data to trajectories. We show the existence of an optimal control which minimizes the quadratic cost function and establish the necessary conditions of optimality of an optimal control fo...

On a Type of Hyperbolic Variational–hemivariational Inequalities

We consider a hyperbolic variational–hemivariational initial value problem on a vector valued functions space. Using a regularization procedure and a Barbu result we obtain an existence result for a problem independent on u′.

On Asymptotic Behavior of Global Solutions for Hyperbolic Hemivariational Inequalities

In this paper we study the existence of global weak solutions for a hyperbolic differential inclusion with a discontinuous and nonlinear multivalued term. Also we investigate the asymptotic behavior of solutions.

Existence and Uniform Decay of Solutions of a Parabolic-Hyperbolic Equation with Nonlinear Boundary Damping and Boundary Source Term