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Contact shape optimization based on the reciprocal variational formulation

Jaroslav Haslinger (1999)

Applications of Mathematics

The paper deals with a class of optimal shape design problems for elastic bodies unilaterally supported by a rigid foundation. Cost and constraint functionals defining the problem depend on contact stresses, i.e. their control is of primal interest. To this end, the so-called reciprocal variational formulation of contact problems making it possible to approximate directly the contact stresses is used. The existence and approximation results are established. The sensitivity analysis is carried out....

Contents

Czesław Olech, Bronisław Jakubczyk, Jerzy Zabczyk (1985)

Banach Center Publications

Continuity of solutions to a basic problem in the calculus of variations

Francis Clarke (2005)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

We study the problem of minimizing ∫ Ω F ( D u ( x ) ) d x over the functions u ∈ W 1 , 1 ( Ω ) that assume given boundary values φ on Γ : = ∂ Ω . The lagrangian F and the domain Ω are assumed convex. A new type of hypothesis on the boundary function φ is introduced: thelower (or upper) bounded slope condition. This condition, which is less restrictive than the familiar bounded slope condition of Hartman, Nirenberg and Stampacchia, allows us to extend the classical Hilbert-Haar regularity theory to the case of semiconvex (or semiconcave) boundary...

Continuous dependence estimates for the ergodic problem of Bellman-Isaacs operators via the parabolic Cauchy problem

Claudio Marchi (2012)

ESAIM: Control, Optimisation and Calculus of Variations

This paper concerns continuous dependence estimates for Hamilton-Jacobi-Bellman-Isaacs operators. We establish such an estimate for the parabolic Cauchy problem in the whole space  [0, +∞) × ℝn and, under some periodicity and either ellipticity or controllability assumptions, we deduce a similar estimate for the ergodic constant associated to the operator. An interesting byproduct of the latter result will be the local uniform convergence for some classes of singular perturbation problems.

Continuous dependence on function parameters for superlinear Dirichlet problems

Aleksandra Orpel (2005)

Colloquium Mathematicae

We discuss the existence of solutions for a certain generalization of the membrane equation and their continuous dependence on function parameters. We apply variational methods and consider the PDE as the Euler-Lagrange equation for a certain integral functional, which is not necessarily convex and coercive. As a consequence of the duality theory we obtain variational principles for our problem and some numerical results concerning approximation of solutions.

Continuous limits of discrete perimeters

Antonin Chambolle, Alessandro Giacomini, Luca Lussardi (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We consider a class of discrete convex functionals which satisfy a (generalized) coarea formula. These functionals, based on submodular interactions, arise in discrete optimization and are known as a large class of problems which can be solved in polynomial time. In particular, some of them can be solved very efficiently by maximal flow algorithms and are quite popular in the image processing community. We study the limit in the continuum of these functionals, show that they always converge...

Continuous-time periodic systems in H 2 and H ∞ . Part I: Theoretical aspects

Patrizio Colaneri (2000)

Kybernetika

The paper is divided in two parts. In the first part a deep investigation is made on some system theoretical aspects of periodic systems and control, including the notions of H 2 and H ∞ norms, the parametrization of stabilizing controllers, and the existence of periodic solutions to Riccati differential equations and/or inequalities. All these aspects are useful in the second part, where some parametrization and control problems in H 2 and H ∞ are introduced and solved.

Continuous-time periodic systems in H 2 and H ∞ . Part II: State feedback problems

Patrizio Colaneri (2000)

Kybernetika

This paper deals with some state-feedback H 2 / H ∞ control problems for continuous time periodic systems. The derivation of the theoretical results underlying such problems has been presented in the first part of the paper. Here, the parametrization and optimization problems in H 2 , H ∞ and mixed H 2 / H ∞ are introduced and solved.

Control for the Sine-Gordon equation

Madalina Petcu, Roger Temam (2004)

ESAIM: Control, Optimisation and Calculus of Variations

In this article we apply the optimal and the robust control theory to the sine-Gordon equation. In our case the control is given by the boundary conditions and we work in a finite time horizon. We present at the beginning the optimal control problem and we derive a necessary condition of optimality and we continue by formulating a robust control problem for which existence and uniqueness of solutions are derived.

Control for the sine-gordon equation

Madalina Petcu, Roger Temam (2010)

ESAIM: Control, Optimisation and Calculus of Variations

In this article we apply the optimal and the robust control theory to the sine-Gordon equation. In our case the control is given by the boundary conditions and we work in a finite time horizon. We present at the beginning the optimal control problem and we derive a necessary condition of optimality and we continue by formulating a robust control problem for which existence and uniqueness of solutions are derived.

Control in obstacle-pseudoplate problems with friction on the boundary. optimal design and problems with uncertain data

Ivan Hlaváček, Ján Lovíšek (2001)

Applicationes Mathematicae

Four optimal design problems and a weight minimization problem are considered for elastic plates with small bending rigidity, resting on a unilateral elastic foundation, with inner rigid obstacles and a friction condition on a part of the boundary. The state problem is represented by a variational inequality and the design variables influence both the coefficients and the set of admissible state functions. If some input data are allowed to be uncertain a new method of reliable solutions is employed....

Control of the continuity equation with a non local flow

Rinaldo M. Colombo, Michael Herty, Magali Mercier (2011)

ESAIM: Control, Optimisation and Calculus of Variations

This paper focuses on the analytical properties of the solutions to the continuity equation with non local flow. Our driving examples are a supply chain model and an equation for the description of pedestrian flows. To this aim, we prove the well posedness of weak entropy solutions in a class of equations comprising these models. Then, under further regularity conditions, we prove the differentiability of solutions with respect to the initial datum and characterize this derivative. A necessary ...

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