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Modèle effectif de couche mince rugueuse périodique sur une structure semi-infinie

Jean-Baptiste Bellet, Gérard Berginc (2013)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Nous étudions l’effet d’une couche mince rugueuse périodique déposée sur une structure semi-infinie, dans le contexte Helmholtz bi-dimensionnel. Formellement, nous obtenons des conditions de transmission équivalentes à l’ordre 1, par des techniques de type homogénéisation. Suivent alors la résolution du problème du milieu effectif éclairé par une onde plane, et le calcul de la fonction de Green effective ; le tout par analyse de Fourier. Dans un deuxième temps, nous considérons le problème de diffraction...

Multi-peak solutions for magnetic NLS equations without non-degeneracy conditions

Silvia Cingolani, Louis Jeanjean, Simone Secchi (2009)

ESAIM: Control, Optimisation and Calculus of Variations

In this work we consider the magnetic NLS equation ( i - A ( x ) ) 2 u + V ( x ) u - f ( | u | 2 ) u = 0 in N ( 0 . 1 ) where N 3 , A : N N is a magnetic potential, possibly unbounded, V : N is a multi-well electric potential, which can vanish somewhere, f is a subcritical nonlinear term. We prove the existence of a semiclassical multi-peak solution u : N to (0.1), under conditions on the nonlinearity which are nearly optimal.

Multi-peak solutions for magnetic NLS equations without non-degeneracy conditions

Silvia Cingolani, Louis Jeanjean, Simone Secchi (2008)

ESAIM: Control, Optimisation and Calculus of Variations

In this work we consider the magnetic NLS equation ( i - A ( x ) ) 2 u + V ( x ) u - f ( | u | 2 ) u = 0 in N ( 0 . 1 ) where N 3 , A : N N is a magnetic potential, possibly unbounded, V : N is a multi-well electric potential, which can vanish somewhere, f is a subcritical nonlinear term. We prove the existence of a semiclassical multi-peak solution u : N to (0.1), under conditions on the nonlinearity which are nearly optimal.

Multiscale analysis of wave propagation in random media. Application to correlation-based imaging

Josselin Garnier (2013/2014)

Séminaire Laurent Schwartz — EDP et applications

We consider sensor array imaging with the purpose to image reflectors embedded in a medium. Array imaging consists in two steps. In the first step waves emitted by an array of sources probe the medium to be imaged and are recorded by an array of receivers. In the second step the recorded signals are processed to form an image of the medium. Array imaging in a scattering medium is limited because coherent signals recorded at the receiver array and coming from a reflector to be imaged are weak and...

Nonlinear boundary value problems with application to semiconductor device equations

Miroslav Pospíšek (1994)

Applications of Mathematics

The paper deals with boundary value problems for systems of nonlinear elliptic equations in a relatively general form. Theorems based on monotone operator theory and concerning the existence of weak solutions of such a system, as well as the convergence of discretized problem solutions are presented. As an example, the approach is applied to the stationary Van Roosbroeck’s system, arising in semiconductor device modelling. A convergent algorithm suitable for solving sets of algebraic equations generated...

Nonlinear models for laser-plasma interaction

Thierry Colin, Mathieu Colin, Guy Métivier (2006/2007)

Séminaire Équations aux dérivées partielles

In this paper, we present a nonlinear model for laser-plasma interaction describing the Raman amplification. This system is a quasilinear coupling of several Zakharov systems. We handle the Cauchy problem and we give some well-posedness and ill-posedness result for some subsystems.

Nonlinear Pulse Propagation

Jeffrey Rauch (2001)

Journées équations aux dérivées partielles

This talk gives a brief review of some recent progress in the asymptotic analysis of short pulse solutions of nonlinear hyperbolic partial differential equations. This includes descriptions on the scales of geometric optics and diffractive geometric optics, and also studies of special situations where pulses passing through focal points can be analysed.

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