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Theoretical and numerical study of a quasi-linear Zakharov system describing Landau damping

R. Belaouar, T. Colin, G. Gallice, C. Galusinski (2007)

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper, we study a Zakharov system coupled to an electron diffusion equation in order to describe laser-plasma interactions. Starting from the Vlasov-Maxwell system, we derive a nonlinear Schrödinger like system which takes into account the energy exchanged between the plasma waves and the electrons via Landau damping. Two existence theorems are established in a subsonic regime. Using a time-splitting, spectral discretizations for the Zakharov system and a finite difference scheme for...

Theoretical aspects and numerical computation of the time-harmonic Green's function for an isotropic elastic half-plane with an impedance boundary condition

Mario Durán, Eduardo Godoy, Jean-Claude Nédélec (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

This work presents an effective and accurate method for determining, from a theoretical and computational point of view, the time-harmonic Green's function of an isotropic elastic half-plane where an impedance boundary condition is considered. This method, based on the previous work done by Durán et al. (cf. [Numer. Math.107 (2007) 295–314; IMA J. Appl. Math.71 (2006) 853–876]) for the Helmholtz equation in a half-plane, combines appropriately analytical and numerical techniques, which has an important...

Theoretical aspects of a multiscale analysis of the eigenoscillations of the Earth.

Volker Michel (2003)

Revista Matemática Complutense

The elastic behaviour of the Earth, including its eigenoscillations, is usually described by the Cauchy-Navier equation. Using a standard approach in seismology we apply the Helmholtz decomposition theorem to transform the Fourier transformed Cauchy-Navier equation into two non-coupled Helmholtz equations and then derive sequences of fundamental solutions for this pair of equations using the Mie representation. Those solutions are denoted by the Hansen vectors Ln,j, Mn,j, and Nn,j in geophysics....

Theoretical foundation of the weighted Laplace inpainting problem

Laurent Hoeltgen, Andreas Kleefeld, Isaac Harris, Michael Breuss (2019)

Applications of Mathematics

Laplace interpolation is a popular approach in image inpainting using partial differential equations. The classic approach considers the Laplace equation with mixed boundary conditions. Recently a more general formulation has been proposed, where the differential operator consists of a point-wise convex combination of the Laplacian and the known image data. We provide the first detailed analysis on existence and uniqueness of solutions for the arising mixed boundary value problem. Our approach considers...

Théorie de la diffusion pour le modèle de Nelson et problème infrarouge

Christian Gérard (2003)

Journées équations aux dérivées partielles

Nous considérons dans cet exposé la théorie de la diffusion pour des modèles de Pauli-Fierz sans masse divergents infrarouge. Nous montrons que les représentations CCR obtenues a partir des champs asymptotiques contiennent des secteurs cohérents décrivant un nombre infini de bosons asymptotiquement libres. Nous formulons quelques conjectures qui conduisent a une notion bien définie de sections efficaces inclusives et non inclusives pour les Hamiltoniens de Pauli-Fierz. Finalement nous donnons une...

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