Integral approach to sensitive singular perturbations
Year: 2009
Type: preprint
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.
Source: arXiv (Cornell University)
Institution: Mathématiques Appliquées à Paris 5
Language: English
Subfield: Numerical Analysis
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4307674147