Sensitive versus classical singular perturbation problem via fourier transform

Mathematical Models and Methods in Applied Sciences

Volumn 16, Issue 11, 2006, Pages 1783-1816

  Meunier, N ^a   Sanchez Palencia, E ^b  

^a UNIVERSITÉ PARIS DAUPHINE   (France)

^b SORBONNE UNIVERSITÉ   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33750731634     PISSN: 02182025     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218202506001716     Document Type: Article

References (21)

1. S. Agmon, A. Douglis and L. Nirenberg, Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions, Comm. Pure Appl. Math. 12 (1959) 623-727.
2. R. Courant and D. Hilbert, Methods of Mathematical Physics (Interscience, 1962), Vol. II.
3. Y. V. Egorov and B. W. Schulze, Pseudodifferential Operators, Singularities and Applications (Birkhäuser, 1997).
4. A. Erdelyi, Asymptotic. Expansions (Dover, 1956).
5. P. Gérard and E. Sanchez-Palencia, Sensitivity phenomena for certain thin elastic shells with edges, Math. Meth. Appl. Sci. 23 (2000) 379-399.
6. S. G. Gindikin and L. R. Volevich, The Cauchy problem, in Encyclopaedia of Mathematical Sciences, Vol. 32 (Springer, 1991), pp. 1-86.
7. I. M. Guelfand and G. E. Chilov, Les Distributions (Dunod, 1962).
8. D. Huet, Phénomènes de perturbation singulière dans les problèmes aux limites, Ann. Inst. Fourier 10 (1960) 61-150.
9. T. Kato, Perturbation Theory for Linear Operators (Springer, 1966).
10. A. I. Komech, Linear partial differential equations with constant coefficients, in Encyclopaedia of Mathematical Sciences, Vol. 31 (Springer, 1994), pp. 121-255.
11. J. L. Lions, Perturbations Singulières dans les Problèmes aux Limites et en Contrôle Optimal (Springer-Verlag, 1973).
12. J.-L. Lions and E. Sanchez-Palencia, Problèmes sensitifs et coques élastiques minces, in Partial, Differential Equations and Functional Analysis, in memory of P. Grisvard, eds. J. Cea, D. Chenais, G. Geymonat and J.-L. Lions (Birkhäuser, 1996), pp. 207-220.
13. J. W. de Roever, Analytic representations and Fourier transforms of analytic functionals in Z′ carried by the real space, SIAM J. Math. Anal. 9 (1978) 996-1019.
14. J. Sanchez Hubert and E. Sanchez-Palencia, Vibration and Coupling of Continuous Systems. Asymptotic Methods (Springer, 1989).
15. J. Sanchez Hubert and E. Sanchez-Palencia, Coques élastiques minces. Propriétés Asymptotiques (Masson, 1997).
16. E. Sanchez-Palencia, Asymptotic and spectral properties of a class of singular-stiff problems, J. Math. Pures Appl. 71 (1992) 379-406.
17. E. Sanchez-Palencia, On the structure of layers for singularly perturbed equations in the case of unbounded energy, Control Optim. Calc. Var. 8 (2002) 941-963.
18. E. Sanchez-Palencia and C. A. de Souza, Complexification phenomenon in an example of sensitive singular perturbation, Comptes Rend. Mec. 332 (2003) 605-612.
19. E. Sanchez-Palencia and C. A. de Souza, Complexification phenomena in certain singular perturbations, in Fluid Mechanics: A Volume in Honor of Amable Linan, eds. F. J. Higuera, A. Jiménez and J. M. Vega (CIMNE, 2004), pp. 363-379.
20. E. Sanchez-Palencia and C. A. de Souza, Complexification in singular perturbations and their approximation, Int. J. Multiscale Comput. Engrg. 3 (2006) 481-498.
21. L. Schwartz, Les Distributions (Hermann, 1961).