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Comparison and existence results for evolutive non-coercive first-order Hamilton-Jacobi equations

Alessandra Cutrì, Francesca Da Lio (2007)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper we prove a comparison result between semicontinuous viscosity subsolutions and supersolutions to Hamilton-Jacobi equations of the form u t + H ( x , D u ) = 0 in I R n × ( 0 , T ) where the Hamiltonian H may be noncoercive in the gradient Du. As a consequence of the comparison result and the Perron's method we get the existence of a continuous solution of this equation.

Comportement semi-classique du spectre des hamiltoniens quantiques elliptiques

Didier Robert, Bernard Helffer (1981)

Annales de l'institut Fourier

Dans cet article nous généralisons les résultats obtenus par J. Chazarain sur le spectre d’opérateurs de Schrödinger P ( h ) = h 2 2 Δ + V lorsque h 0 . Nous étendons ses résultats aux opérateurs pseudo-différentiels globalement elliptiques d’ordre m > 0 .

Composite control of the n -link chained mechanical systems

Jiří Zikmund (2008)

Kybernetika

In this paper, a new control concept for a class of underactuated mechanical system is introduced. Namely, the class of n -link chains, composed of rigid links, non actuated at the pivot point is considered. Underactuated mechanical systems are those having less actuators than degrees of freedom and thereby requiring more sophisticated nonlinear control methods. This class of systems includes among others frequently used for the modeling of walking planar structures. This paper presents the stabilization...

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