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Rainer Picard (1992)
Banach Center Publications
The paper considers the static Maxwell system for a Lipschitz domain with perfectly conducting boundary. Electric and magnetic permeability ε and μ are allowed to be monotone and Lipschitz continuous functions of the electromagnetic field. The existence theory is developed in the framework of the theory of monotone operators.
Di Pomponio, Stefania (2000)
Serdica Mathematical Journal
The author is partially supported by: M. U. R. S. T. Prog. Nazionale “Problemi e Metodi nella Teoria delle Equazioni Iperboliche”.We treat the oscillatory problem for semilinear wave equation. The oscillatory initial data are of the type u(0, x) = h(x) + ε^(σ+1) * e^(il(x)/ε) * b0 (ε, x) ∂t u(0, x) = ε^σ * e^(il(x)/ε) * b1(ε, x). By using suitable variants of Strichartz estimate we extend the results from [6] on a priori estimates of the approximations of geometric optics.The main improvement...
Castro, L.P. (2002)
JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]
Machado, J., Jesus, Isabel (2004)
Fractional Calculus and Applied Analysis
Mathematics Subject Classification: 26A33 (main), 35A22, 78A25, 93A30The generalization of the concept of derivative to non-integer values goes back to the beginning of the theory of differential calculus. Nevertheless, its application in physics and engineering remained unexplored up to the last two decades. Recent research motivated the establishment of strategies taking advantage of the Fractional Calculus (FC) in the modeling and control of many phenomena. In fact, many classical engineering...
Giovanni Crupi (1958)
Bollettino dell'Unione Matematica Italiana
E. Virga (1983)
Rendiconti del Seminario Matematico della Università di Padova
Jan Brandts (1999)
Applications of Mathematics
We will show that some of the superconvergence properties for the mixed finite element method for elliptic problems are preserved in the mixed semi-discretizations for a diffusion equation and for a Maxwell equation in two space dimensions. With the help of mixed elliptic projection we will present estimates global and pointwise in time. The results for the Maxwell equations form an extension of existing results. For both problems, our results imply that post-processing and a posteriori error estimation...
A. Liapounoff (1898)
Journal de Mathématiques Pures et Appliquées
J. Moutier (1875)
Nouvelles annales de mathématiques : journal des candidats aux écoles polytechnique et normale
Gouy (1882)
Journal de Mathématiques Pures et Appliquées
Mascart (1877)
Annales scientifiques de l'École Normale Supérieure
Gérard Gagneux, Olivier Millet (2014)
Annales de la faculté des sciences de Toulouse Mathématiques
Le système d’évolution de Nernst-Planck-Poisson-Boltzmann modélise les transferts ioniques en milieu poreux saturé en prenant en compte des interactions électrocapillaires au contact du substrat. Ce modèle présente un intérêt particulier en génie civil pour étudier la dégradation par corrosion des matériaux cimentaires, à structure micro-locale périodique, sous l’effet des ions chlorures. Les techniques d’homogénéisation sont alors un outil puissant pour élaborer un modèle macroscopique équivalent...
M. Ferraris, M. Francaviglia, C. Reina (1983)
Annales de l'I.H.P. Physique théorique
Boussinesq, J. (1872)
Journal de Mathématiques Pures et Appliquées
M. Mascart (1872)
Annales scientifiques de l'École Normale Supérieure
Mascart (1874)
Annales scientifiques de l'École Normale Supérieure
Christophe Cheverry (2008/2009)
Séminaire Équations aux dérivées partielles
Cet exposé s’intéresse à un modèle réaliste issu de la mécanique des fluides. L’objectif est de montrer qu’il est possible de traiter dans un tel cadre des problèmes d’instabilité soulevés par la propagation de singularités qualifiées de surcritiques. D’abord, nous introduisons le modèle (équations de type Navier-Stokes) et ses motivations (questions liées à la propagation d’oscillations en régime turbulent). Ensuite, nous présentons deux résultats (relatifs au caractère bien posé d’un problème...
A. Martin (1881)
Annales scientifiques de l'École Normale Supérieure
Alain Joets, Ahmed Belaidi, Roland Ribotta (2003)
Banach Center Publications
Physical systems producing caustics may possess symmetries. In that case the relation between the symmetry of the system, considered as a whole, and the symmetry of the caustic follow a very general symmetry principle, the Curie principle. We give various examples of application of the Curie principle to caustics produced by the deflection of light in liquid crystals: the so called squint effect, the visualization of a new type of roll structure, etc. We show also that the Curie principle applies...
Serge Piperno (2006)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
The Discontinuous Galerkin Time Domain (DGTD) methods are now popular for the solution of wave propagation problems. Able to deal with unstructured, possibly locally-refined meshes, they handle easily complex geometries and remain fully explicit with easy parallelization and extension to high orders of accuracy. Non-dissipative versions exist, where some discrete electromagnetic energy is exactly conserved. However, the stability limit of the methods, related to the smallest elements in the mesh,...