Displaying similar documents to “Non-smoothness in the asymptotics of thin shells and propagation of singularities. Hyperbolic case”

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

E. Sanchez–Palencia (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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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...

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

Similarity:

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...

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

Petar Popivanov, Iordan Iordanov (2003)

Banach Center Publications

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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.

Singularities of eddy current problems

Martin Costabel, Monique Dauge, Serge Nicaise (2003)

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

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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...

Singularities in drawings of singular surfaces

Alain Joets (2008)

Banach Center Publications

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When drawing regular surfaces, one creates a concrete and visual example of a projection between two spaces of dimension 2. The singularities of the projection define the apparent contour of the surface. As a result there are two types of generic singularities: fold and cusp (Whitney singularities). The case of singular surfaces is much more complex. A priori, it is expected that new singularities may appear, resulting from the "interaction" between the singularities of the surface and...