Catálogo de publicaciones - libros

The minimization of drag functional for the stationary, isothermal, compressible Navier-Stokes equations (N-S-E) in three spatial dimensions is considered. In order to establish the existence of an optimal shape the general result [] on compactness of families of generalized solutions to N-S-E is applied. The family of generalized solutions to N-S-E is constructed over a family of admissible domains . Any admissible domain Ω = contains an obstacle , e.g., a wing profile. Compactness properties of the family of admissible domains are imposed. It turns out that we require the compactness of the family of admissible domains with respect to the Hausdorff metrics as well as in the sense of Kuratowski-Mosco. The analysis is performed for the range of adiabatic ratio > 1 in the pressure law () = and it is based on the technique proposed in [] for the discretized N-S-E.

The feedback stabilization of the Navier-Stokes equations around an unstable stationary solution is related to the feedback stabilization of the Oseen equations (the linearized Navier-Stokes equations about the unstable stationary solution). In this paper we investigate the regularizing properties of feedback operators corresponding to a family of optimal control problems for the Oseen equations.

Quantum control is traditionally expressed through bilinear models and their associated Lie algebra controllability criteria. But, the first order approximation are not always sufficient and higher order developments are used in recent works. Motivated by these applications, we give in this paper a criterion that applies to situations where the evolution operator is expressed as sum of possibly non-linear real functionals of the control that multiplies some time independent (coupling) operators.

We investigate optimal control problems with vector-valued controls. As model problem serve the optimal distributed control of the instationary Navier-Stokes equations. We study pointwise convex control constraints, which is a constraint of the form () ∈ () that has to hold on the domain . Here, is an set-valued mapping that is assumed to be measurable with convex and closed images. We establish first-order necessary as well as second-order sufficient optimality conditions. And we prove regularity results for locally optimal controls.

This paper deals with the control of a moving dynamical domain in which a non cylindrical dynamical boundary value problem is considered. We consider weak Eulerian evolution of domains through the convection of a measurable set by (non necessarily smooth) vector field . We introduce the concept of tubes by “product space” and we show a closure result leading to existence results for a variational shape principle. We illustrate this by new results: heat equation and wave equation in moving domains with various boundary conditions and also the geodesic characterisation for two Eulerian shape metrics leading to the Euler equation through the transverse field considerations. We consider the non linear Hamilton-Jacobi like equation associated with level set parametrization of the moving domain and give new existence result of possible topological change in finite time in the solution.