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Nicolas Meunier; Jacqueline Sanchez-Hubert; Évariste Sanchez-Palencia
Various kinds of sensitive singular perturbations
Annales mathématiques Blaise Pascal, 14 no. 2 (2007), p. 199-242, doi: 10.5802/ambp.233
Article PDF | Reviews MR 2369872 | Zbl 1153.35011

Résumé - Abstract

We consider variational problems of P. D. E. depending on a small parameter $\varepsilon $ when the limit process $\varepsilon \downarrow 0$ implies vanishing of the higher order terms. The perturbation problem is said to be sensitive when the energy space of the limit problem is out of the distribution space, so that the limit problem is out of classical theory of P. D. E. We present here a review of the subject, including abstract convergence theorems and two very different model problems (the second one is presented for the first time). For each one we prove the sensitive character and we give a formal asymptotics for the behavior $\varepsilon \downarrow 0$.

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