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Averaging of boundary value problems with a singular perturbation of the boundary conditions

G. A. Chechkin


Abstract: Boundary value problems with different conditions on alternating small parts of the boundary are considered. An investigation is made of the behavior of solutions of such problems as the small parameter characterizing the period of change of the type of the boundary conditions goes to zero, and estimates are given for the deviation of these solutions from the solutions of the limit problem in various cases. The spectral properties of these problems are studied from a unified point of view on the basis of general methods (see [4], [9]).

UDC: 517.9

MSC: Primary 35J25, 35J05; Secondary 73K10, 35B25

Received: 23.04.1992

 English version: Russian Academy of Sciences. Sbornik. Mathematics, 1994, 79:1, 191–222

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