In this paper we summarize a dual-time scale formulation of dynamic user equilibrium with demand growth due to Friesz et al (2008). This formulation belongs to the problem class that Pang and Stewart (2008) refer to as di¤erential variational inequalities. We also present a …xed point algorithm for computing solutions to the dual time-scale model without calculating derivatives, along with a nu...

A self-consistent scheme based on the calculus of infinitesimal transformations that describes model based interpolation (MBI hereafter) of high dimensional data, constrained to lie on a nonlinear manifold, is expressed as a dynamical system. The variational formulation derived for a single cluster is extended to the case of finite mixture models (FMM hereafter). The suggested formulation is sh...

In this paper, size dependent beam type peizoelectric energy hardvester is investigated. For this goal, first nonlinear formulation of isotropic piezoelectric Euler-Bernoulli nano-beam is developed based on the size-dependent piezoelectricity theory then special beam type piezoelectric energy hardvester is probed for different parameters. Basic nonlinear equations of piezoelectric nano-beam are...

A 3D slip-dependent frictional contact problem in elastostatics is discussed. We deliver a variational formulation as a mixed variational problem whose Lagrange multipliers set is solutiondependent. Then, the existence and the boundedness of the solutions is investigated. The proof is based on a recent result for an abstract mixed variational problem with solution-dependent set of Lagrange mult...

This paper presents general variational formulations for dynamical problems, which are easily implemented numerically. The development presents the relationship between the very general weak formulation arismg from linear and angular momentum balance considerations, and well known variational priciples. Two and three field mixed forms are developed from the general weak form. The variational pr...

Abstract. In this paper we present the first results on substructuring methods for nonlocal operators, specifically, an instance of the nonlocal p-Laplace operator. We present a nonlocal variational formulation of this operator, proving a nonlocal Poincaré inequality and upper bound to establish a spectral equivalence. We then introduce a nonlocal two-domain variational formulation utilizing no...

We consider variational inequalities with different trial and test spaces and a possibly non-coercive bilinear form. Well-posedness is shown under general conditions that are e.g. valid for the space-time variational formulation of parabolic variational inequalities. Moreover, we prove an estimate for the error of a Petrov-Galerkin approximation in terms of the residual. For parabolic variation...

It is well known that the Wiener-Hopf equations are equivalent to the general variational inequalities. We use this alternative equivalent formulation to study the sensitivity of the general variational inequalities without assuming the differentiability of the given data. Since the general variational inequalities include classical variational inequalities and complementarity problems as speci...

Recently, Galley [1] proposed an initial value problem formulation of Hamilton’s principle applied to non-conservative systems. Here, we explore this formulation for complex partial differential equations of the nonlinear Schrödinger (NLS) type, examining the dynamics of the coherent solitary wave structures of such models by means of a non-conservative variational approximation (NCVA). We comp...

We consider the problem of scattering of time harmonic acoustic waves by an unbounded sound soft surface which is assumed to lie within a finite distance of some plane. The paper is concerned with the study of an equivalent variational formulation of this problem set in a scale of weighted Sobolev spaces. We prove well-posedness of this variational formulation in an energy space with weights wh...