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Strong stabilization of controlled vibrating systems

Jean-François Couchouron (2011)

ESAIM: Control, Optimisation and Calculus of Variations

This paper deals with feedback stabilization of second order equations of the form ytt + A0y + u (t) B0y (t) = 0, t ∈ [0, +∞[, where A0 is a densely defined positive selfadjoint linear operator on a real Hilbert space H, with compact inverse and B0 is a linear map in diagonal form. It is proved here that the classical sufficient ad-condition of Jurdjevic-Quinn and Ball-Slemrod with the feedback control u = ⟨yt, B0y⟩H implies the strong stabilization. This result is derived from a general compactness...

Strong stabilization of controlled vibrating systems

Jean-François Couchouron (2011)

ESAIM: Control, Optimisation and Calculus of Variations

This paper deals with feedback stabilization of second order equations of the form ytt + A0y + u (t) B0y (t) = 0, t ∈ [0, +∞[, where A0 is a densely defined positive selfadjoint linear operator on a real Hilbert space H, with compact inverse and B0 is a linear map in diagonal form. It is proved here that the classical sufficient ad-condition of Jurdjevic-Quinn and Ball-Slemrod with the feedback control u = ⟨yt, B0y⟩H implies the strong stabilization. This result is derived from a general compactness theorem...

Sur un problème parabolique-elliptique

Philippe Benilan, Petra Wittbold (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We prove existence (uniqueness is easy) of a weak solution to a boundary value problem for an equation like ( v - 1 ) t + = v x x + F ( v ) x where the function F : is only supposed to be locally lipschitz continuous. In order to replace the lack of compactness in t on v<1, we use nonlinear semigroup theory.

The Kneser property for the abstract Cauchy problem

Hernán R. Henríquez, Genaro Castillo G. (2003)

Annales Polonici Mathematici

We establish existence of mild solutions for the semilinear first order functional abstract Cauchy problem and we prove that the set of mild solutions of this problem is connected in the space of continuous functions.

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