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

ESAIM: Control, Optimisation and Calculus of Variations (2002)

- Volume: 8, page 941-963
- ISSN: 1292-8119

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topSanchez-Palencia, E.. "On the structure of layers for singularly perturbed equations in the case of unbounded energy." ESAIM: Control, Optimisation and Calculus of Variations 8 (2002): 941-963. <http://eudml.org/doc/245292>.

@article{Sanchez2002,

abstract = {We consider singular perturbation variational problems depending on a small parameter $ \varepsilon $. The right hand side is such that the energy does not remain bounded as $ \varepsilon \rightarrow 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 $ \varepsilon >0 $ are elliptic. In the parabolic and hyperbolic cases, the propagation of singularities appear as an integral property after integrating across the layers.},

author = {Sanchez-Palencia, E.},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {singular perturbations; unbounded energy; propagation of singularities; distribution right hand sides},

language = {eng},

pages = {941-963},

publisher = {EDP-Sciences},

title = {On the structure of layers for singularly perturbed equations in the case of unbounded energy},

url = {http://eudml.org/doc/245292},

volume = {8},

year = {2002},

}

TY - JOUR

AU - Sanchez-Palencia, E.

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

JO - ESAIM: Control, Optimisation and Calculus of Variations

PY - 2002

PB - EDP-Sciences

VL - 8

SP - 941

EP - 963

AB - We consider singular perturbation variational problems depending on a small parameter $ \varepsilon $. The right hand side is such that the energy does not remain bounded as $ \varepsilon \rightarrow 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 $ \varepsilon >0 $ are elliptic. In the parabolic and hyperbolic cases, the propagation of singularities appear as an integral property after integrating across the layers.

LA - eng

KW - singular perturbations; unbounded energy; propagation of singularities; distribution right hand sides

UR - http://eudml.org/doc/245292

ER -

## References

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- [6] P. Karamian, J. Sanchez–Hubert and E. Sanchez–Palencia, Propagation of singularities and structure of the layers in shells. Hyperbolic case. Comp. and Structures (to appear).
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- [11] E. Sanchez–Palencia, Singular perturbations going out of the energy space. Layers in elliptic and parabolic cases, in Proc. of the 4th european Conference on Elliptic and Parabolic Problems. Rolduc-Gaeta, edited by Bemelmans et al. World Scientific Press (2002). Zbl1033.35010
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