Strong solutions for some nonlinear partial functional differential equations with infinite delay.
Strong stabilization of controlled vibrating systems
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
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
Sur un problème parabolique-elliptique
We prove existence (uniqueness is easy) of a weak solution to a boundary value problem for an equation like where the function 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.
Symmetry operators of a Hartree-type equation with quadratic potential.