Displaying similar documents to “On the structure of layers for singularly perturbed equations in the case of unbounded energy”

On the structure of layers for singularly perturbed equations in the case of unbounded energy

E. Sanchez-Palencia (2002)

ESAIM: Control, Optimisation and Calculus of Variations


We consider singular perturbation variational problems depending on a small parameter ε . The right hand side is such that the energy does not remain bounded as ε 0 . The asymptotic behavior involves internal layers where most of the energy concentrates. Three examples are addressed, with limits elliptic, parabolic and hyperbolic respectively, whereas the problems with ε > 0 are elliptic. In the parabolic and hyperbolic cases, the propagation of singularities appear as an integral property after...

Non-smoothness in the asymptotics of thin shells and propagation of singularities. Hyperbolic case

Philippe Karamian, Jacqueline Sanchez-Hubert, Évariste Sanchez Palencia (2002)

International Journal of Applied Mathematics and Computer Science


We consider the limit behaviour of elastic shells when the relative thickness tends to zero. We address the case when the middle surface has principal curvatures of opposite signs and the boundary conditions ensure the geometrical rigidity. The limit problem is hyperbolic, but enjoys peculiarities which imply singularities of unusual intensity. We study these singularities and their propagation for several cases of loading, giving a somewhat complete description of the solution. ...

On the anomalous singularities of the solutions to some classes of weakly hyperbolic semilinear systems. Examples

Petar Popivanov, Iordan Iordanov (2003)

Banach Center Publications


This paper deals with the newly observed singularities of the solutions of some specific examples of weakly hyperbolic semilinear systems in R². Two, respectively three, characteristics are supposed to be mutually tangential at the origin only and the initial data are continuous only. The exact strength of the new-born singularities is investigated too.

Quasilinear waves and trapping: Kerr-de Sitter space

Peter Hintz, András Vasy (2014)

Journées Équations aux dérivées partielles


In these notes, we will describe recent work on globally solving quasilinear wave equations in the presence of trapped rays, on Kerr-de Sitter space, and obtaining the asymptotic behavior of solutions. For the associated linear problem without trapping, one would consider a global, non-elliptic, Fredholm framework; in the presence of trapping the same framework is available for spaces of growing functions only. In order to solve the quasilinear problem we thus combine these frameworks...

Preface, Contents

Stanisław Janeczko, Wojciech Zajączkowski, Bogdan Ziemian (1996)

Banach Center Publications


Singularities of eddy current problems

Martin Costabel, Monique Dauge, Serge Nicaise (2003)

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


We consider the time-harmonic eddy current problem in its electric formulation where the conductor is a polyhedral domain. By proving the convergence in energy, we justify in what sense this problem is the limit of a family of Maxwell transmission problems: Rather than a low frequency limit, this limit has to be understood in the sense of Bossavit [11]. We describe the singularities of the solutions. They are related to edge and corner singularities of certain problems for the scalar...