Integral approach to sensitive singular perturbations

2009/10/12 by Nicolas Meunier, Meunier, Nicolas, Evariste Sanchez-Palencia +1
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP

paper · pdf · doi:10.48550/arxiv.0910.2087

arxiv created 2009/10/12 · arxiv updated 2016/11/25

Abstract

We consider singular perturbation elliptic problems depending on a parameter ? such that, for ? = 0 the boundary conditions are not adapted to the equation (they do not satisfy the Shapiro - Lopatinskii condition). The limit only holds in very abstract spaces out of distribution theory involving complexi?cation and non-local phenomena. We give a very elementary model problem showing the main features of the limit process, as well as a heuristic integral procedure for obtain- ing a description of the solutions for small ?. Such kind of problems appear in thin shell theory when the middle surface is elliptic and the shell is fixed by a part of the boundary and free by the rest.

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