Maz'ya, Vladimir, Movchan, Alexander and Nieves, Michael
(2010)
Mesoscale asymptotic approximations to solutions of mixed boundary value
problems in perforated domains.
SIAM: Multiscale Modeling and Simulation.
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Abstract
We describe a method of asymptotic approximations to solutions of mixed boundary value problems for the Laplacian in a three-dimensional domain with many perforations of arbitrary shape, with the Neumann boundary conditions being prescribed on the surfaces of small voids. The only assumption made on the geometry is that the diameter of a void is assumed to be smaller compared to the distance to the nearest neighbour. The asymptotic approximation, obtained here, involves a linear combination of dipole fields constructed for individual voids, with the coefficients, which are determined by solving a linear algebraic system. We prove the solvability of this system and derive an estimate for its solution. The energy estimate is obtained for the remainder term of the asymptotic approximation.
| Item Type: | Article |
|---|---|
| Additional Information: | 20 pages, 8 figures |
| Uncontrolled Keywords: | math-ph, math-ph, math.MP |
| Depositing User: | Symplectic Admin |
| Date Deposited: | 21 Dec 2017 15:48 |
| Last Modified: | 19 Jan 2023 06:46 |
| Related URLs: | |
| URI: | https://livrepository.liverpool.ac.uk/id/eprint/3014627 |
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