We consider singular perturbation variational problems depending on a small parameter . The right hand side is such that the energy does not remain bounded as . 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 are elliptic. In the parabolic and hyperbolic cases, the propagation of singularities appear as an integral property after integrating across the layers.
Mots clés : singular perturbations, unbounded energy, propagation of singularities
@article{COCV_2002__8__941_0,
author = {Sanchez-Palencia, E.},
title = {On the structure of layers for singularly perturbed equations in the case of unbounded energy},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {941--963},
publisher = {EDP-Sciences},
volume = {8},
year = {2002},
doi = {10.1051/cocv:2002043},
zbl = {1070.35005},
language = {en},
url = {http://www.numdam.org/articles/10.1051/cocv:2002043/}
}
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 SP - 941 EP - 963 VL - 8 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv:2002043/ DO - 10.1051/cocv:2002043 LA - en ID - COCV_2002__8__941_0 ER -
%0 Journal Article %A Sanchez-Palencia, E. %T On the structure of layers for singularly perturbed equations in the case of unbounded energy %J ESAIM: Control, Optimisation and Calculus of Variations %D 2002 %P 941-963 %V 8 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv:2002043/ %R 10.1051/cocv:2002043 %G en %F COCV_2002__8__941_0
Sanchez-Palencia, E. On the structure of layers for singularly perturbed equations in the case of unbounded energy. ESAIM: Control, Optimisation and Calculus of Variations, Tome 8 (2002), pp. 941-963. doi : 10.1051/cocv:2002043. http://www.numdam.org/articles/10.1051/cocv:2002043/
[1] , Asymptotic analysis of singular perturbations. North-Holland, Amsterdam (1979). | MR | Zbl
[2] and, Les distributions. Dunod, Paris (1962). | MR | Zbl
[3] and, Sensitivity phenomena for certain thin elastic shells with edges. Math. Meth. Appl. Sci. 23 (2000) 379-399. | Zbl
[4] , Matching of asymptotic expansions of solutions of boundary value problems. Amer. Math. Soc. (1991).
[5] and, Boundary layers in thin elastic shells with developable middle surface. Eur. J. Mech., A/Solids 21 (2002) 13-47. | Zbl
[6] , and, Propagation of singularities and structure of the layers in shells. Hyperbolic case. Comp. and Structures (to appear).
[7] , Perturbations singulières dans les problèmes aux limites et en contrôle optimal. Springer, Berlin (1973). | MR | Zbl
[8] and, Problèmes aux limites non homogènes et applications, Vol. 1. Dunod, Paris (1968). | MR | Zbl
[9] and, Sensitivity of certain constrained systems and application to shell theory. J. Math. Pures Appl. 79 (2000) 821-838. | Zbl
[10] , On a singular perturbation going out of the energy space. J. Math. Pures. Appl. 79 (2000) 591-602. | Zbl
[11] , 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). | Zbl
[12] and, Regular degenerescence and boundary layer for linear differential equations with small parameter.Usp. Mat. Nauk 12 (1957) 1-122. | Zbl
Cité par Sources :
