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

ESAIM - Control, Optimisation and Calculus of Variations

Volumn 8, Issue , 2002, Pages 941-963

  Sanchez Palencia, E ^a  

^a SORBONNE UNIVERSITÉ   (France)

Author keywords

Propagation of singularities; Singular perturbations; Unbounded energy

Indexed keywords

ASYMPTOTIC ANALYSIS; CONTROL SYSTEM ANALYSIS; PROBLEM SOLVING;

ELLIPTIC; HYPERBOLIC; PARABOLIC; SINGULAR PERTURBATION VARIATIONAL PROBLEMS; UNBOUNDED ENERGY;

PERTURBATION TECHNIQUES;

EID: 0344793016     PISSN: 12928119     EISSN: 12623377     Source Type: Journal    
DOI: 10.1051/cocv:2002043     Document Type: Article

References (12)

1. W. Eckhaus, Asymptotic analysis of singular perturbations. North-Holland, Amsterdam (1979).
2. I.M. Guelfand and G.E. Chilov, Les distributions. Dunod, Paris (1962).
3. P. Gérard and E. Sanchez-Palencia, Sensitivity phenomena for certain thin elastic shells with edges. Math. Meth. Appl. Sci. 23 (2000) 379-399.
4. A.M. Il'in, Matching of asymptotic expansions of solutions of boundary value problems. Amer. Math. Soc. (1991).
5. P. Karamian and J. Sanchez-Hubert, Boundary layers in thin elastic shells with developable middle surface. Eur. J. Mech., A/Solids 21 (2002) 13-47.
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).
7. J.-L. Lions, Perturbations singulières dans les problèmes aux limites et en contrôle optimal. Springer, Berlin (1973).
8. J.-L. Lions and E. Magenes, Problèmes aux limites non homogènes et applications, Vol. 1. Dunod, Paris (1968).
9. J.-L. Lions and E. Sanchez-Palencia, Sensitivity of certain constrained systems and application to shell theory. J. Math. Pures Appl. 79 (2000) 821-838.
10. E. Sanchez-Palencia, On a singular perturbation going out of the energy space. J. Math. Pures. Appl. 79 (2000) 591-602.
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).
12. M.I. Vishik and L. Lusternik, Regular degenerescence and boundary layer for linear differential equations with small parameter. Usp. Mat. Nauk 12 (1957) 1-122.