This article is cited in 12 papers

Asymptotic solution of the Signorini problem with an obstacle on a thin elongated set

I. I. Argatov^a, S. A. Nazarov<sup>b

a</sup> Saint-Petersburg State University
^b Admiral Makarov State Maritime Academy

Abstract: The Signorini problem for a Poisson equation is studied subject to onesided constraints imposed on a narrow annular boundary band $\Gamma _\varepsilon$ (of width $O(\varepsilon )$). An asymptotic analysis yields a resultant variational inequality on the contour $\Gamma$ to which $\Gamma _\varepsilon$ contracts as $\varepsilon \to 0$. Approximate solutions of the resultant inequality are derived with varying degree of accuracy and used to construct and justify an asymptotic solution of the original Signorini problem.

UDC: 517.953

MSC: Primary 35C20; Secondary 35B20, 35J85

Received: 10.02.1995

DOI: 10.4213/sm162

 English version: Sbornik: Mathematics, 1996, 187:10, 1411–1442

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