Well-posedness for Systems Representing Electromagnetic/Acoustic Wavefront Interaction

Well-posedness of Hybrid Systems

Well-Posedness for a One-Dimensional Fluid-Particle Interaction Model

The fluid-particle interaction model introduced by the three last authors in [J. Differential Equations, 245 (2008), pp. 3503–3544] is the object of our study. This system consists of the Burgers equation with a singular source term (term that models the interaction via a drag force with a moving point particle) and of an ODE for the particle path. The notion of entropy solution for the singula...

Well{posedness of Stiff Hyperbolic Systems

The theory of stii well{posedness of initial value problems for hyperbolic systems with large relaxation terms is reviewed. Furthermore, an asymptotic expansion of solutions with respect to the relaxation parameter is presented. Finally, the theory is illustrated with an example and an outlook concerning boundary value problems is given.

Global Well-posedness of Nls-kdv Systems for Periodic Functions

We prove that the Cauchy problem of the Schrödinger-KortewegdeVries (NLS-KdV) system for periodic functions is globally well-posed for initial data in the energy space H1×H1. More precisely, we show that the nonresonant NLS-KdV system is globally well-posed for initial data in Hs(T) × Hs(T) with s > 11/13 and the resonant NLS-KdV system is globally wellposed with s > 8/9. The strategy is to app...

Hamiltonian identification for quantum systems : well posedness and numerical approaches

This paper considers the inversion problem related to the manipulation of quantum systems using laser-matter interactions. The focus is on the identification of the field free Hamiltonian and/or the dipole moment of a quantum system. The evolution of the system is given by the Schrödinger equation. The available data are observations as a function of time corresponding to dynamics generated by ...