Francisco Periago

Optimal shape and position of the support for the internal exact control of a string

Abstract In this paper, we consider the problem of optimizing the shape and position of the support ω of the internal exact control of minimal L 2 ( 0 , T ; L 2 ( ω ) ) -norm for the 1-D wave equation. A relaxation for this problem is found and the minimizers of the relaxed problem are characterized through first-order optimality conditions.

Long Time Behavior of a Two-Phase Optimal Design for the Heat Equation

We consider a two-phase isotropic optimal design problem within the context of the transient heat equation. The objective is to minimize the average of the dissipated thermal energy during a fixed time interval

Global existence, uniqueness, and continuous dependence for a semilinear initial value problem☆

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Numerical approximation of bang-bang controls for the heat equation: an optimal design approach

. The time-independent material properties are taken as design variables. A full relaxation for this problem was established in [A. Munch, P. Pedregal, and F. Periago, J. Math. Pures Appl. (9), 89 (2008), pp. 225-247] by using the homogenization method. In this paper, we study the asymptotic behavior as

Robust Averaged Control of Vibrations for the Bernoulli–Euler Beam Equation

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Some remarks on homogenization and exact boundary controllability for the one-dimensional wave equation

goes to infinity of the solutions of the relaxed problem and prove that they converge to an optimal relaxed design of the corresponding two-phase optimization problem for the stationary heat equation. Next we study necessary optimality conditions for the relaxed optimization problem under the transient heat equation and use those to characterize the microstructure of the optimal designs, which appears in the form of a sequential laminate of rank at most

Optimal Design of the Time-Dependent Support of Bang---Bang Type Controls for the Approximate Controllability of the Heat Equation

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Robust Optimal Design of Quantum Electronic Devices

, the spatial dimension. An asymptotic analysis of the optimality conditions lets us prove that, for

Una herramienta de simulación numérica para el análisis de la capacidad de maniobrabilidad de un submarino

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A First Step towards Variational Methods in Engineering.

large enough, the order of lamination is, in fact, of at most