Dual extremum principles for a homogeneous Dirichlet problem for a parabolic equation.
The dual variational formulation of some free boundary value problem is given and its approximation by finite element method is studied, using piecewise linear elements with non-positive divergence.
La programación lineal sobre subconjuntos difusos, definida por Zimmermann, se desarrolla en estrecha relación con la definición de las funciones pertinentes funciones de pertenencia. Se estudia la dualidad difusa, ligada a la dualidad en los problemas de programación lineal con multicriterios.
The present article explores the way -approximated method is applied to substantiate duality results for the fractional variational problems under invexity. -approximated dual pair is engineered and a careful study of the original dual pair has been done to establish the duality results for original problems. Moreover, an appropriate example is constructed based on which we can validate the established dual statements. The paper includes several recent results as special cases.
The paper presents a problem of duality for the obstacle and unilateral biharmonic problem (the equilibrium of a thin plate with an obstacle inside the domain or on the boundary). The dual variational inequality is derived by introducing polar functions.
A dual-weighted residual approach for goal-oriented adaptive finite elements for a class of optimal control problems for elliptic variational inequalities is studied. The development is based on the concept of C-stationarity. The overall error representation depends on primal residuals weighted by approximate dual quantities and vice versa as well as various complementarity mismatch errors. Also, a priori bounds for C-stationary points and associated multipliers are derived. Details on the numerical...
We consider dynamic problems which describe frictional contact between a body and a foundation. The constitutive law is viscoelastic or elastic and the frictional contact is modelled by a general subdifferential condition on the velocity, including the normal damped responses. We derive weak formulations for the models and prove existence and uniqueness results. The proofs are based on the theory of second-order evolution variational inequalities. We show that the solutions of the viscoelastic problems...
This paper studies the dynamic coverage control problem for cooperative region reconnaissance where a group of agents are required to reconnoitre a given region. The main challenge of this problem is that the sensing region of each agent is an ellipse. This modeling results in asymmetric(directed) interactions among agents. First, the region reconnaissance is formulated as a coverage problem, where each point in the given region should be surveyed until a preset level is achieved. Then, a coverage...
We solve an optimal cost problem for a stochastic Navier-Stokes equation in space dimension 2 by proving existence and uniqueness of a smooth solution of the corresponding Hamilton-Jacobi-Bellman equation.
The purpose of this paper is to present an alternative proof of the existence of the Walrasian equilibrium for the Arrow-Debreu-McKenzie model by the variational inequality technique. Moreover, examples of the generalized Arrow-Debreu-McKenzie model are given in which the price vector can reach the boundary of the orthant allowing a commodity to be of price zero at equilibrium. In such a case its supply exceeds demand. It is worth mentioning that utility functions in this model are allowed not to...
In this paper we deal with the energy functionals for the elastic thin film ω ⊂ ℝ² involving the bending moments. The effective energy functional is obtained by Γ-convergence and 3D-2D dimension reduction techniques. Then we prove the existence of minimizers of the film energy functional. These results are proved in the case when the energy density function has the growth prescribed by an Orlicz convex function M. Here M is assumed to be non-power-growth-type and to satisfy the conditions Δ₂ and...
In this paper we consider an elastic thin film ω ⊂ ℝ² with the bending moment depending also on the third thickness variable. The effective energy functional defined on the Orlicz-Sobolev space over ω is described by Γ-convergence and 3D-2D dimension reduction techniques. Then we prove the existence of minimizers of the film energy functional. These results are proved in the case when the energy density function has the growth prescribed by an Orlicz convex function M. Here M is assumed to be non-power-growth-type...