Problème aux limites pour le système de Vlasov-Maxwell
Programming of the generalized nonlinear paraxial equation for the formation of solitons with Mathematica.
Prolongation loop algebras for a solitonic system of equations.
Propagation of electromagnetic waves in non-homogeneous media
We consider electromagnetic waves propagating in a periodic medium characterized by two small scales. We perform the corresponding homogenization process, relying on the modelling by Maxwell partial differential equations.
Propagation, reflection and refraction of singularities for a hyperbolic transmission problem in two adjacent angular regions
Properties of a quasi-uniformly monotone operator and its application to the electromagnetic $p$-$\text {curl}$ systems
In this paper we propose a new concept of quasi-uniform monotonicity weaker than the uniform monotonicity which has been developed in the study of nonlinear operator equation $Au=b$. We prove that if $A$ is a quasi-uniformly monotone and hemi-continuous operator, then $A^{-1}$ is strictly monotone, bounded and continuous, and thus the Galerkin approximations converge. Also we show an application of a quasi-uniformly monotone and hemi-continuous operator to the proof of the well-posedness and convergence...
Properties of certain improper integrals
Proposition de préconditionneurs pseudo-différentiels pour l’équation CFIE de l’électromagnétisme
We present a weak parametrix of the operator of the CFIE equation. An interesting feature of this parametrix is that it is compatible with different discretization strategies and hence allows for the construction of efficient preconditioners dedicated to the CFIE. Furthermore, one shows that the underlying operator of the CFIE verifies an uniform discrete Inf-Sup condition which allows to predict an original convergence result of the numerical solution of the CFIE to the exact one.
Proposition de préconditionneurs pseudo-différentiels pour l'équation CFIE de l'électromagnétisme
On exhibe dans cette note une paramétrix (au sens faible) de l'opérateur sous-jacent à l'équation CFIE de l'électromagnétisme. L'intérêt de cette paramétrix est de se prêter à différentes stratégies de discrétisation et ainsi de pouvoir être utilisée comme préconditionneur de la CFIE. On montre aussi que l'opérateur sous-jacent à la CFIE satisfait une condition Inf-Sup discrète uniforme, applicable aux espaces de discrétisation usuellement rencontrés en électromagnétisme, et qui permet d'établir...
Quasilinear hyperbolic equations with hysteresis
Radiation effect on MHD free-convection flow of a gas at a stretching surface with a uniform free stream.
Radiation reaction, renormalization and Poincaré symmetry.
Radiaton effects on unsteady MHD free convection with Hall current near an infinite vertical porous plate.
Raman laser : mathematical and numerical analysis of a model
In this paper we study a discrete Raman laser amplification model given as a Lotka-Volterra system. We show that in an ideal situation, the equations can be written as a Poisson system with boundary conditions using a global change of coordinates. We address the questions of existence and uniqueness of a solution. We deduce numerical schemes for the approximation of the solution that have good stability.
Raman laser: mathematical and numerical analysis of a model
In this paper we study a discrete Raman laser amplification model given as a Lotka-Volterra system. We show that in an ideal situation, the equations can be written as a Poisson system with boundary conditions using a global change of coordinates. We address the questions of existence and uniqueness of a solution. We deduce numerical schemes for the approximation of the solution that have good stability.
Random Schrödinger operators with a constant electric field
Recherches sur la dispersion anomale
Recherches sur le pouvoir réfringent des liquides
Reconstruction of thickness variation of a dielectric coating through the generalized impedance boundary conditions
We deal with an inverse scattering problem whose aim is to determine the thickness variation of a dielectric thin coating located on a conducting structure of unknown shape. The inverse scattering problem is solved through the application of the Generalized Impedance Boundary Conditions (GIBCs) which contain the thickness, curvature as well as material properties of the coating and they have been obtained in the previous work [B. Aslanyürek, H. Haddar and H.Şahintürk, Wave Motion 48 (2011) 681–700]...
Recovering quantum graphs from their Bloch spectrum
We define the Bloch spectrum of a quantum graph to be the map that assigns to each element in the deRham cohomology the spectrum of an associated magnetic Schrödinger operator. We show that the Bloch spectrum determines the Albanese torus, the block structure and the planarity of the graph. It determines a geometric dual of a planar graph. This enables us to show that the Bloch spectrum indentifies and completely determines planar -connected quantum graphs.