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We study the Dirichlet boundary value problem for eikonal type equations of ray light propagation in an inhomogeneous medium with discontinuous refraction index. We prove a comparison principle that allows us to obtain existence and uniqueness of a continuous viscosity solution when the Lie algebra generated by the coefficients satisfies a Hörmander type condition. We require the refraction index to be piecewise continuous across Lipschitz hypersurfaces. The results characterize the value...

Derivation of the Zakharov equations

Benjamin Texier (2005)

Journées Équations aux dérivées partielles

Diffraction des singularités analytiques dans les problèmes aux limites de la physique mathématique par les méthodes de Kawai-Kashiwara et Sjöstrand

Wuidar, José (1982)

Portugaliae mathematica

Diffraction par un convexe.

Thierry Harge, Gilles Lebeau (1994)

Inventiones mathematicae

Diffraction spectra of weighted Delone sets on beta-lattices with beta a quadratic unitary Pisot number

Jean-Pierre Gazeau, Jean-Louis Verger-Gaugry (2006)

Annales de l’institut Fourier

The Fourier transform of a weighted Dirac comb of beta-integers is characterized within the framework of the theory of Distributions, in particular its pure point part which corresponds to the Bragg part of the diffraction spectrum. The corresponding intensity function on this Bragg part is computed. We deduce the diffraction spectrum of weighted Delone sets on beta-lattices in the split case for the weight, when beta is the golden mean.

Diffractive nonlinear geometric optics

P. Donnat, J.-L. Joly, G. Métivier, J. Rauch (1995/1996)

Séminaire Équations aux dérivées partielles (Polytechnique)

Diffusion électromagnétique à basse fréquence par un réseau de cylindres diélectriques. Étude numérique

B. Ducomet, D. Ha. Quang (1992)

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

Diffusion électromagnétique à basse fréquence par un réseau de cylindres diélectriques

B. Ducomet (1992)

Annales de l'I.H.P. Physique théorique

Diodový detektor s filtrem

Stanislav Vojtášek (1961)

Aplikace matematiky

Dioptrika se stanoviska vyšší geometrie [I.]

Josef Hervert (1872)

Časopis pro pěstování mathematiky a fysiky

Dioptrika se stanoviska vyšší geometrie [II.]

Josef Hervert (1872)

Časopis pro pěstování mathematiky a fysiky

Dioptrika se stanoviska vyšší geometrie [III.]

Josef Hervert (1872)

Časopis pro pěstování mathematiky a fysiky

Direct current electric potential in an anisotropic half-space with vertical contact containing a conductive 3D body.

Li, Ping, Stagnitti, Frank (2004)

Mathematical Problems in Engineering

Discrete compactness for a discontinuous Galerkin approximation of Maxwell's system

Emmanuel Creusé, Serge Nicaise (2006)

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper we prove the discrete compactness property for a discontinuous Galerkin approximation of Maxwell's system on quite general tetrahedral meshes. As a consequence, a discrete Friedrichs inequality is obtained and the convergence of the discrete eigenvalues to the continuous ones is deduced using the theory of collectively compact operators. Some numerical experiments confirm the theoretical predictions.

Distinguished Riemann-Hamilton geometry in the polymomentum electrodynamics

Alexandru Oană, Mircea Neagu (2012)

Communications in Mathematics

In this paper we develop the distinguished (d-) Riemannian differential geometry (in the sense of d-connections, d-torsions, d-curvatures and some geometrical Maxwell-like and Einstein-like equations) for the polymomentum Hamiltonian which governs the multi-time electrodynamics.

Div-curl lemma revisited: Applications in electromagnetism

Marián Slodička, Ján Jr. Buša (2010)

Kybernetika

Two new time-dependent versions of div-curl results in a bounded domain $Ω \subset ℝ^{3}$ are presented. We study a limit of the product $v_{k} w_{k}$ , where the sequences $v_{k}$ and $w_{k}$ belong to $Ł_{2} (Ω)$ . In Theorem 2.1 we assume that $\nabla \times v_{k}$ is bounded in the $L_{p}$ -norm and $\nabla \cdot w_{k}$ is controlled in the $L_{r}$ -norm. In Theorem 2.2 we suppose that $\nabla \times w_{k}$ is bounded in the $L_{p}$ -norm and $\nabla \cdot w_{k}$ is controlled in the $L_{r}$ -norm. The time derivative of $w_{k}$ is bounded in both cases in the norm of $- 1 (Ω)$ . The convergence (in the sense of distributions) of $v_{k} w_{k}$ to the product $v w$ of weak limits...

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