This paper deals with the formulation of a necessary optimality condition for a topology optimization problem for an elastic contact problem with Tresca friction. In the paper a quasistatic contact model is considered, rather than a stationary one used in the literature. The functional approximating the normal contact stress is chosen as the shape functional. The aim of the topology optimizatio...

Let K be a nonempty closed convex subset of a reflexive and strictly convex Banach space E with a uniformly Gâteaux differentiable norm, F {T h : h ≥ 0} a generalized asymptotically nonexpansive self-mapping semigroup of K, and f : K → K a fixed contractive mapping with contractive coefficient β ∈ 0, 1 . We prove that the following implicit and modified implicit viscosity iterative schemes {xn}...

Extending the characterization of the directional derivatives of a strongly regular solution to a variational inequality under parameter perturbations, this paper derives a first-order sensitivity result for a monotone-plus affine variational inequality (AVI) having non-isolated solutions. The result employs a “directional AVI” whose solutions provide the directional derivatives, if they exist,...

In this paper we study the distributed optimal control for the Cahn–Hilliard system. A general class of free energy potentials is allowed which, in particular, includes the double-obstacle potential. The latter potential yields an optimal control problem of a parabolic variational inequality which is of fourth order in space. We show the existence of optimal controls to approximating problems w...

The purpose of this work is to carry out the analysis of twodimensional scalar variational problems by the method of moments. This method is indeed shown to be useful for treating general cases in which the Lagrangian is a separable polynomial in the derivative variables. In these cases, it follows that the discretization of these problems can be reduced to a single large scale semidefinite pro...

Abstract The generalized Broer-Kaup-Kupershmidt (generalized BKK) isospectral problem, including the x-derivative of potential, is considered based on Lie algebra A1. The variational trace identity is extended to construct Hamiltonian structure of generalized BKK system. The Lie algebra A1 is extended to the non-semi-simple Lie algebra of 4 × 4 matrix form, from which a hierarchy of soliton equ...

In this work, we propose a Crank-Nicolson-type scheme with variable steps for the time fractional Allen-Cahn equation. The proposed is shown to be unconditionally stable (in variational energy sense), and maximum bound preserving. Interestingly, discrete stability result obtained in paper can recover classical dissipation law when order $\alpha \rightarrow 1.$ That is, our asymptotically preser...

In this paper, we propose the new concept of optimal solution for fuzzy variational problems based on the possibility and necessity measures. Inspired by the well–known embedding theorem, we can transform the fuzzy variational problem into a bi–objective variational problem. Then the optimal solutions of fuzzy variational problem can be obtained by solving its corresponding biobjective variatio...

Princeton University, Princeton, NJ This paper desribes a technique for finding the numerical solution of the Full Potential equation for steady transonic flow about airfoils. The exterior but finite domain is discretized by breaking it up into triangles. Difference equations are formulated using variational principle and a formula for the derivative in an arbitrary polygon. The iterative schem...

A general iteration formula of variational iteration method (VIM) for fractional heatand wave-like equations with variable coefficients is derived. Compared with previous work, the Lagrange multiplier of the method is identified in a more accurate way by employing Laplace’s transform of fractional order.The fractional derivative is considered in Jumarie’s sense.The results are more accurate tha...