Optimal control systems by time-dependent coefficients using CAS wavelets.
Optimal design problems for a dynamic viscoelastic plate. I. Short memory material
We deal with an optimal control problem with respect to a variable thickness for a dynamic viscoelastic plate with velocity constraints. The state problem has the form of a pseudohyperbolic variational inequality. The existence and uniqueness theorem for the state problem and the existence of an optimal thickness function are proved.
Optimal energy decay rate of coupled wave equations.
Optimal feedback control of a class of distributed-parameter systems with incomplete measurement
Optimal grids for anisotropic problems.
Optimal internal dissipation of a damped wave equation using a topological approach
We consider a linear damped wave equation defined on a two-dimensional domain Ω, with a dissipative term localized in a subset ω. We address the shape design problem which consists in optimizing the shape of ω in order to minimize the energy of the system at a given time T . By introducing an adjoint problem, we first obtain explicitly the (shape) derivative of the energy at time T with respect to the variation in ω. Expressed as a boundary integral on ∂ω, this derivative is then used as an advection...
Optimal LQ-feedback control for a class of first-order hyperbolic distributed parameter systems
The Linear-Quadratic (LQ) optimal control problem is studied for a class of first-order hyperbolic partial differential equation models by using a nonlinear infinite-dimensional (distributed parameter) Hilbert state-space description. First the dynamical properties of the linearized model around some equilibrium profile are studied. Next the LQ-feedback operator is computed by using the corresponding operator Riccati algebraic equation whose solution is obtained via a related matrix Riccati differential...
Optimality conditions for a Bolza problem governed by a hyperbolic system of Darboux-Goursat type
Optimization problems for structural acoustic models with thermoelasticity and smart materials
Optimization problem for a structural acoustic model with controls governed by unbounded operators on the state space is considered. This type of controls arises naturally in the context of "smart material technology". The main result of the paper provides an optimal synthesis and solvability of associated nonstandard Riccati equations. It is shown that in spite of the unboundedness of control operators, the resulting gain operators (feedbacks) are bounded on the state space. This allows to provide...
Optique Géométrique et invariance de jauge : Solutions oscillantes d’amplitude critique pour les équations de Yang-Mills
Optique géométrique non linéaire et équations de Maxwell-Bloch
Optique géométrique oscillante en présence d'un grand choc
Optique non linéaire et ondes sur critiques
Oscillating Multipliers for some Eigenfunction Expansions.
Oscillation criteria for nonlinear inhomogeneous hyperbolic equations with distributed deviating arguments.
Oscillation of nonlinear impulsive hyperbolic equations with several delays.
Oscillation of solutions for systems of hyperbolic equations of neutral type.
Oscillations fortes sur un champ linéairement dégénéré
Oscillations non linéaires des systèmes hyperboliques : méthodes et résultats qualitatifs
Oscillations of anharmonic Fourier series and the wave equation.
In this paper we have collected some partial results on the sign of u(t,x) where u is a (sufficiently regular) solution of⎧ utt + (-1)m Δmu = 0 (t,x) ∈ R x Ω⎨⎩ u|Γ = ... = Δm-1 u|Γ = 0 t ∈ R.These results rely on the study of a sign of almost periodic functions of a special form restricted to a bounded interval J.