For a large class of real-valued potentials, V (x), x ∈ R, n ≥ 4 , we prove dispersive estimates for the low frequency part of e Pac, provided the zero is neither an eigenvalue nor a resonance of −∆+ V , where Pac is the spectral projection onto the absolutely continuous spectrum of −∆ + V . This class includes potentials V ∈ L(R) satisfying V (x) = O ( 〈x〉−(n+2)/2−ǫ ) , ǫ > 0. As a consequence...

In the present work, certain aspects, restricted to the visual system, of the J. Gonzalo’s research, are interpreted according to a simple linear theory of time-dispersion applied to the dynamic cerebral system, characterized by its excitability and its reaction velocity.

The non-retarded dispersive force between an electrically polarizable atom and a magnetically polarizable one

Article history: Received 20 November 2015 Received in revised form 8 March 2016 Accepted 25 March 2016 Available online 31 March 2016

Based on Whitham’s variational approach and employing the 4× 4 formalism for dispersive wave motion, new balance and conservation laws were established. The general relations are illustrated with a specific example. © 2005 Elsevier B.V. All rights reserved.

The first purpose of this note is to provide a proof of the usual square function estimate on L(Ω). It turns out to follow directly from a generic Mikhlin multiplier theorem obtained by Alexopoulos, which mostly relies on Gaussian bounds on the heat kernel. We also provide a simple proof of a weaker version of the square function estimate, which is enough in most instances involving dispersive ...

Laboratory experiments have shown that when nonlinear, dispersive waves are forced periodically from one end of an undisturbed stretch of the medium of propagation, the signal eventually becomes temporally periodic at each spatial point. It is our purpose here to establish this as a fact at least in the context of a damped Korteweg-de Vries equation. Thus, consideration is given to the initial-...

We show existence of global solutions for the gravity water waves equation in dimension 3, in the case of small data. The proof combines energy estimates, which yield control of L related norms, with dispersive estimates, which give decay in L∞. To obtain these dispersive estimates, we use an analysis in Fourier space; the study of space and time resonances is then the crucial point.

We study the Whitham equations for the defocusing complex modified KdV (mKdV) equation. These Whitham equations are quasilinear hyperbolic equations and they describe the averaged dynamics of the rapid oscillations which appear in the solution of the mKdV equation when the dispersive parameter is small. The oscillations are referred to as dispersive shocks. The Whitham equations for the mKdV eq...

Approved: Thesis Supervisor Title and Department