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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 integrating...

On the membrane approximation for thin elastic shells in the hyperbolic case.

E. Sánchez-Palencia — 1993

Revista Matemática de la Universidad Complutense de Madrid

We consider the variational formulation of the problem of elastic shells in the membrane approximation, when the medium surface is hyperbolic. It appears that the corresponding bilinear form behaves as some kind of two-dimensional elasticity without shear rigidity. This amounts to saying that the membrane behaves rather as a net made of elastic strings disposed along the asymptotic curves of the surface than as an elastic two-dimensional medium. The mathematical and physical reasons of this behavior...

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

E. SanchezPalencia — 2010

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...

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