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Paradoxes of Limit Passage in Solutions of Boundary Value Problems When Smooth Domains Are Approximated by Polygons

Identifieur interne : 000221 ( Main/Exploration ); précédent : 000220; suivant : 000222

Paradoxes of Limit Passage in Solutions of Boundary Value Problems When Smooth Domains Are Approximated by Polygons

Auteurs : Vladimir Maz A [Suède] ; Serguei A. Nazarov [Russie] ; Boris A. Plamenevskij [Russie]

Source :

Operator Theory ; 2000.

RBID : ISTEX:BCABA96639AABA9DC0E25F1E147CD274F48E376F

Abstract

Abstract: In the present chapter we approximate smooth domains by polygonal ones and analyze passing to the limit in solutions of boundary value problems. For this purpose we use an asymptotic approach. Though the techniques have a broader field of applications, we restrict ourselves to studying some particular boundary value problems in the theory of thin plates. More precisely, we consider a number of questions related to the known paradox that goes back to Sapondzhyan [2] and Babuška [2]. The case in point is the following example of instability: if one makes approximations of a thin circular plate by regular polygons with freely supported boundaries, one obtains the limiting solution that does not satisfy the freely supporting condition. We explain the asymptotic genesis of the Sapondzhyan-Babuska paradox, point a way to eliminate it and reveal some new phenomena of instability.

Url:

https://api.istex.fr/document/BCABA96639AABA9DC0E25F1E147CD274F48E376F/fulltext/pdf

DOI: 10.1007/978-3-0348-8432-7_8

Affiliations:

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<front><div type="abstract" xml:lang="en">Abstract: In the present chapter we approximate smooth domains by polygonal ones and analyze passing to the limit in solutions of boundary value problems. For this purpose we use an asymptotic approach. Though the techniques have a broader field of applications, we restrict ourselves to studying some particular boundary value problems in the theory of thin plates. More precisely, we consider a number of questions related to the known paradox that goes back to Sapondzhyan [2] and Babuška [2]. The case in point is the following example of instability: if one makes approximations of a thin circular plate by regular polygons with freely supported boundaries, one obtains the limiting solution that does not satisfy the freely supporting condition. We explain the asymptotic genesis of the Sapondzhyan-Babuska paradox, point a way to eliminate it and reveal some new phenomena of instability.</div>
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Paradoxes of Limit Passage in Solutions of Boundary Value Problems When Smooth Domains Are Approximated by Polygons

Paradoxes of Limit Passage in Solutions of Boundary Value Problems When Smooth Domains Are Approximated by Polygons

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Abstract

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