Displaying similar documents to “On necessary conditions in the calculus of variations.”

Relaxation of optimal control problems in 𝖫 𝗉 -spaces

Nadir Arada (2001)

ESAIM: Control, Optimisation and Calculus of Variations

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We consider control problems governed by semilinear parabolic equations with pointwise state constraints and controls in an L p -space ( p < ∞ ). We construct a correct relaxed problem, prove some relaxation results, and derive necessary optimality conditions.

How to state necessary optimality conditions for control problems with deviating arguments?

Lassana Samassi, Rabah Tahraoui (2008)

ESAIM: Control, Optimisation and Calculus of Variations

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The aim of this paper is to give a general idea to state optimality conditions of control problems in the following form: inf ( u , v ) ∈ 𝒰 a d ∫ 0 1 f t , u ( θ v ( t ) ) , u ' ( t ) , v ( t ) d t , (1) where 𝒰 a d is a set of admissible controls and θ v is the solution of the following equation: { d θ ( t ) d t = g ( t , θ ( t ) , v ( t ) ) , t ∈ [ 0 , 1 ] ; θ ( 0 ) = θ 0 , θ ( t ) ∈ [ 0 , 1 ] ∀ t . (2). The results are nonlocal and new.

Convergence and asymptotic stabilization for some damped hyperbolic equations with non-isolated equilibria

Felipe Alvarez, Hedy Attouch (2001)

ESAIM: Control, Optimisation and Calculus of Variations

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It is established convergence to a particular equilibrium for weak solutions of abstract linear equations of the second order in time associated with monotone operators with nontrivial kernel. Concerning nonlinear hyperbolic equations with monotone and conservative potentials, it is proved a general asymptotic convergence result in terms of weak and strong topologies of appropriate Hilbert spaces. It is also considered the stabilization of a particular equilibrium via the introduction...