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Singular perturbation for the Dirichlet boundary control of elliptic problems

Faker Ben Belgacem, Henda El Fekih, Hejer Metoui (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

A current procedure that takes into account the Dirichlet boundary condition with non-smooth data is to change it into a Robin type condition by introducing a penalization term; a major effect of this procedure is an easy implementation of the boundary condition. In this work, we deal with an optimal control problem where the control variable is the Dirichlet data. We describe the Robin penalization, and we bound the gap between the penalized and the non-penalized boundary controls for the small...

Singularités éliminables pour des équations semi-linéaires

Pierre Baras, Michel Pierre (1984)

Annales de l'institut Fourier

Étant donné L un opérateur différentiel d’ordre m sur un ouvert Ω de R N , K un compact de Ω , γ > 1 et γ ' = γ / ( γ - 1 ) , nous montrons que toute solution de “ L u + u γ = 0 sur Ω ∖ K , u ≥ 0 ” est solution de “ L u + u γ = 0 sur Ω ” dès que la W m , γ ' -capacité de K est nulle. Cette condition s’avère nécessaire quand L est un opérateur elliptique d’ordre 2. Dans ce cas, nous montrons aussi que ` ` L u + u | u | γ - 1 = μ , u | ∂ Ω = 0 ' ' où μ est une mesure de Radon bornée sur Ω , a une solution si et seulement si μ ne charge pas les ensembles de W 2 , γ ' -capacité nulle.

Singularities of Maxwell’s system in non-hilbertian Sobolev spaces

Wided Chikouche, Serge Nicaise (2008)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

We study the regularity of the solution of the regularized electric Maxwell problem in a polygonal domain with data in L p ( Ω ) 2 . Using a duality method, we prove a decomposition of the solution into a regular part in the non-Hilbertian Sobolev space W 2 , p ( Ω ) 2 and an explicit singular one.

Sistemi iperbolici di leggi di conservazione

Alberto Bressan (2000)

Bollettino dell'Unione Matematica Italiana

This survey paper provides a brief introduction to the mathematical theory of hyperbolic systems of conservation laws in one space dimension. After reviewing some basic concepts, we describe the fundamental theorem of Glimm on the global existence of BV solutions. We then outline the more recent results on uniqueness and stability of entropy weak solutions. Finally, some major open problems and research directions are discussed in the last section.

Slopes of hypergeometric systems of codimension one.

María Isabel Hartillo Hermoso (2003)

Revista Matemática Iberoamericana

We describe the slopes, with respect to the coordinates hyperplanes, of the hypergeometric systems of codimension one, that is when the toric ideal is generated by one element.

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