Rigorous and heuristic treatment of sensitive singular perturbations arising in elliptic shells

Details Rigorous and heuristic treatment of sensitive singular perturbations arising in elliptic shells Rigorous and heuristic treatment of sensitive singular perturbations arising in elliptic shells

2009-10-12

arxiv.org/abs/0910.2086v1

Mathematics

Analysis of PDEs

Scientific paper

We consider singular perturbations of elliptic systems 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 holds only in very abstract spaces out of distribu- tion theory involving complexi?cation and non-local phenomena. This system appears in the thin shell theory when the middle surface is el- liptic and the shell is ?xed on a part of the boundary and free on the rest. We use a heuristic reasoning applying some simpli?cations which allow to reduce the original problem in a domain to another problem on its boundary. The novelty of this work is that we consider systems of partial di?erential equations while in our previous work we were dealing with single equations.

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