MESOSCALE ASYMPTOTIC APPROXIMATIONS TO SOLUTIONS OF MIXED BOUNDARY VALUE PROBLEMS IN PERFORATED DOMAINS
2011 (English)In: MULTISCALE MODELING and SIMULATION, ISSN 1540-3459, Vol. 9, no 1, 424-448 p.Article in journal (Refereed) Published
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 neighbor. 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.
Place, publisher, year, edition, pages
Siam , 2011. Vol. 9, no 1, 424-448 p.
mesoscale approximation, singular perturbation, multiply perforated domain
Medical and Health Sciences
IdentifiersURN: urn:nbn:se:liu:diva-67552DOI: 10.1137/100791294ISI: 000288988900017OAI: oai:DiVA.org:liu-67552DiVA: diva2:411253
Vladmir Maz'ya, A Movchan and M Nieves, MESOSCALE ASYMPTOTIC APPROXIMATIONS TO SOLUTIONS OF MIXED BOUNDARY VALUE PROBLEMS IN PERFORATED DOMAINS, 2011, MULTISCALE MODELING and SIMULATION, (9), 1, 424-448.