Oscillations non linéaires des systèmes hyperboliques : méthodes et résultats qualitatifs
Oscillations of a nonlinearly damped extensible beam
It is proved that any weak solution to a nonlinear beam equation is eventually globally oscillatory, i.e., there is a uniform oscillatory interval for large times.
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.
Oscillations of higher order differential equations of neutral type
In this paper, sufficient conditions have been obtained for oscillation of solutions of a class of th order linear neutral delay-differential equations. Some of these results have been used to study oscillatory behaviour of solutions of a class of boundary value problems for neutral hyperbolic partial differential equations.
Oscillations of the solutions of nonlinear hyperbolic equations of neutral type.
In this paper nonlinear hyperbolic equations of neutral type of a given form are considered, with certain boundary conditions. Under certain constraints on the coefficients of the equation and the boundary conditions, sufficient conditions for oscillation of the solutions of the problems considered are obtained.
Oscillatory and Fourier integral operators with degenerate canonical relations.
We survey results concerning the L2 boundedness of oscillatory and Fourier integral operators and discuss applications. The article does not intend to give a broad overview; it mainly focuses on topics related to the work of the authors.[Proceedings of the 6th International Conference on Harmonic Analysis and Partial Differential Equations, El Escorial (Madrid), 2002].
Oscillatory and periodic solutions to a diffusion equation of neutral type.
Oscillatory Integrals and the Method of Stationary Phase in Infinitely Many Dimensions, with Applications to the Classical Limit of Quantum Mechanics. I.
Oscillatory integrals with polynomial phases.
Oscillatory limits with varying spectrum
High time frequency oscillations occur in many different physical cases: slightly compressible fluids, almost quasineutral plasmas, small electron mass approximation .... In many case, small parameters arise in fluids mechanics or plasma physics, leading to these oscillations as the small parameter goes to zero. The aim of this note is to detail how to obtain formal expansions and to give some indications on how to justify them.
Oscillatory property of solutions for -Laplacian equations.
Osservazione sulla risolubilità del problema di Dirichlet per una classe di equazioni ellittiche a coefficienti discontinui
Ostrowski type inequalities related to the generalized Baouendi-Grushin vector fields
Otto Vejvoda passed away
Output feedback stabilization of a one-dimensional wave equation with an arbitrary time delay in boundary observation
The stabilization with time delay in observation or control represents difficult mathematical challenges in the control of distributed parameter systems. It is well-known that the stability of closed-loop system achieved by some stabilizing output feedback laws may be destroyed by whatever small time delay there exists in observation. In this paper, we are concerned with a particularly interesting case: Boundary output feedback stabilization of a one-dimensional wave equation system for which the...
Output feedback stabilization of a one-dimensional wave equation with an arbitrary time delay in boundary observation∗
The stabilization with time delay in observation or control represents difficult mathematical challenges in the control of distributed parameter systems. It is well-known that the stability of closed-loop system achieved by some stabilizing output feedback laws may be destroyed by whatever small time delay there exists in observation. In this paper, we are concerned with a particularly interesting case: Boundary output feedback stabilization of a...
Output feedback stabilization of a one-dimensional wave equation with an arbitrary time delay in boundary observation∗
The stabilization with time delay in observation or control represents difficult mathematical challenges in the control of distributed parameter systems. It is well-known that the stability of closed-loop system achieved by some stabilizing output feedback laws may be destroyed by whatever small time delay there exists in observation. In this paper, we are concerned with a particularly interesting case: Boundary output feedback stabilization of a...
Ouverts concaves et théorèmes de dualité pour les systèmes différentiels à coefficients constants
Ouverts stablement convexes par rapport à un opérateur différentiel
On montre l’équivalence entre certaines inégalités “à la Carleman” et certaines propriétés de régularité des solutions à support compact d’équations aux dérivées partielles à coefficients constants : étant un opérateur différentiel sur , on en déduit une caractérisation, en termes d’inégalités , des ouverts de tels que soit -convexe pour tout entier .
Overdetermined hyperbolic systems on l.e. convex sets