Abstract We consider a Cauchy problem for fractional differential inclusion defined by Caputo type derivative and we obtain sufficient condition local controllability along reference trajectory in terms of certain variational associated to the initial problem.

The variational reconstruction theory from a companion paper finds a solution consistent with some linear constraints and minimizing a quadratic plausibility criterion. It is suitable for treating vector and multidimensional signals. Here, we apply the theory to a generalized sampling system consisting of a multichannel filterbank followed by a nonuniform sampling. We provide ready-made formula...

We consider the gradient flow of a one-homogeneous functional, whose dual involves the derivative of a constrained scalar function. We show in this case that the gradient flow is related to a weak, generalized formulation of a Hele-Shaw flow. The equivalence follows from a variational representation, which is a variant of well-known variational representations for the Hele-Shaw problem. As a co...

We study the rigidity of polyhedral surfaces using variational principle. The action functionals are derived from the cosine laws. The main focus of this paper is on the cosine law for a non-triangular region bounded by three possibly disjoint geodesics. Several of these cosine laws were first discovered and used by Fenchel and Nielsen. By studying the derivative of the cosine laws, we discover...

A topological derivative is defined, which is caused by kinking of a crack, thus, representing the topological change. Using variational methods, the anti-plane model of a solid subject to a non-penetration condition imposed at the kinked crack is considered. The objective function of the potential energy is expanded with respect to the diminishing branch of the incipient crack. The respective ...

Traditionally variational level set model for image segmentation is solved by using gradient descent method, which has low computational efficiency and needs complex re-initialization of level set functions as signed distance functions. In this paper, we first reformulate the variational model as a constrained optimization problem. Then we present an augmented Lagrangian projection method to pr...

We consider a second-order elliptic eigenvalue problem on a convex polygonal domain, divided in M nonoverlapping subdomains. The conormal derivative of the unknown function is continuous on the interfaces, while the function itself is discontinuous. We present a general finite element method to obtain a numerical solution of the eigenvalue problem, starting from a nonstandard formally equivalen...

In this paper, variational iteration method (VIM) is applied to solve nonlinear oscillators of fractional order. The time-fractional derivatives are described in the Jumarie’s derivative sense. The application of variational iteration method, developed for differential equations of integer order, is extended to derive explicit analytical solutions of the fractional order nonlinear oscillator’s ...

We study the rigidity of polyhedral surfaces using variational principle. The action functionals are derived from the cosine laws. The main focus of this paper is on the cosine law for a non-triangular region bounded by three possibly disjoint geodesics. Several of these cosine laws were first discovered and used by Fenchel and Nielsen. By studying the derivative of the cosine laws, we discover...

In this paper we investigate optimal control problems governed by variational inequalities. We give optimality conditions under classical assumptions using a dual regularized functional to interpret the Variational Inequality. 1. Introduction. In this paper we investigate optimal control problems governed by vari-ational inequalities of obstacle type. This problem has been widely studied during...