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4 papers · 2 filters
Exponential stability of solutions to the Schr{ö}dinger-Poisson equation
Joackim Bernier, Nicolas Camps, Benoît Grébert +1
We prove an exponential stability result for the small solutions of the Schr{ö}dinger-Poisson equation on the circle without exterior parameters in Gevrey class. More precisely we…
Asymptotic initial value representation of the solutions of semi-classical systems presenting smooth codimension one crossings
Clotilde Fermanian Kammerer, Caroline Lasser, Didier Robert
This paper is devoted to the construction of approximations of the propagator associated with a semi-classical matrix-valued Schrödinger operator with symbol presenting smooth eige…
Dynamics of quintic nonlinear Schr{ö}dinger equations in
Joackim Bernier, Benoît Grébert, Tristan Robert
In this paper, we succeed in integrating Strichartz estimates (encoding the dispersive effects of the equations) in Birkhoff normal form techniques. As a consequence, we deduce a r…
Frequency domain approach for the stability analysis of a fast hyperbolic PDE coupled with a slow ODE
Gonzalo Arias, Swann Marx, Guilherme Mazanti
This paper deals with the exponential stability of systems made of a hyperbolic PDE coupled with an ODE with different time scales, the dynamics of the PDE being much faster than t…