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On the Friedrichs inequality in a domain perforated aperiodically along the boundary. Homogenization procedure. Asymptotics for parabolic problems. (English) Zbl 1180.35072

The focus is the investigation of a boundary-value problem posed in a domain perforated aperiodically (with circular holes) along the boundary for the case when the diameters of the circles and the distance between them are of the same order. The authors derive for such a non-periodic scenario a useful Friederichs-type inequality for functions vanishing on the boundary of the perforations. They also prove the convergence of the oscillatory solutions to the homogenized (non-oscillatory) solution. A numerical illustration concludes the paper.

MSC:

35B27 Homogenization in context of PDEs; PDEs in media with periodic structure
35K20 Initial-boundary value problems for second-order parabolic equations
35B45 A priori estimates in context of PDEs
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