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Operator estimates for non-periodically perforated domains: disappearance of cavities

Operator estimates for non-periodically perforated domains: disappearance of cavities We consider a boundary value problem for a general second-order linear equation in a perforated domain. The perforation is made by small cavities, a minimal distance between the cavities is also small. We impose minimal natural geometric conditions on the shapes of the cavities and no conditions on their distribution in the domain. On the boundaries of the cavities, a nonlinear Robin condition is imposed. The sizes of the cavities and the minimal distance between them are supposed to satisfy a certain simple condition ensuring that under the homogenization the cavities disappear and we obtain a similar problem in a non-perforated domain. Our main results state the convergence of the solution of the perturbed problem to that of the homogenized one in $ W_2^1 $ W 2 1 - and $ L_2 $ L 2 -norms uniformly in $ L_2 $ L 2 -norm of the right-hand side in the equation and provide the estimates for the convergence rates. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applicable Analysis Taylor & Francis

Operator estimates for non-periodically perforated domains: disappearance of cavities

Applicable Analysis , Volume 103 (5): 15 – Mar 23, 2024
15 pages

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References (27)

Publisher
Taylor & Francis
Copyright
© 2023 Informa UK Limited, trading as Taylor & Francis Group
ISSN
0003-6811
eISSN
1563-504X
DOI
10.1080/00036811.2023.2209726
Publisher site
See Article on Publisher Site

Abstract

We consider a boundary value problem for a general second-order linear equation in a perforated domain. The perforation is made by small cavities, a minimal distance between the cavities is also small. We impose minimal natural geometric conditions on the shapes of the cavities and no conditions on their distribution in the domain. On the boundaries of the cavities, a nonlinear Robin condition is imposed. The sizes of the cavities and the minimal distance between them are supposed to satisfy a certain simple condition ensuring that under the homogenization the cavities disappear and we obtain a similar problem in a non-perforated domain. Our main results state the convergence of the solution of the perturbed problem to that of the homogenized one in $ W_2^1 $ W 2 1 - and $ L_2 $ L 2 -norms uniformly in $ L_2 $ L 2 -norm of the right-hand side in the equation and provide the estimates for the convergence rates.

Journal

Applicable AnalysisTaylor & Francis

Published: Mar 23, 2024

Keywords: Perforated domain; non-periodic perforation; operator estimates; convergence rate; 35B27; 35B40

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