4 papers
Asymptotic analysis of solutions to transmission problems in solids with many inclusions
Michael Nieves
We construct an asymptotic approximation to the solution of a transmission problem for a body containing a region occupied by many small inclusions. The cluster of inclusions is ch…
Meso-scale models and approximate solutions for solids containing clouds of voids
Vladimir Maz'ya, Alexander Movchan, Michael Nieves
For highly perforated domains the paper addresses a novel approach to study mixed boundary value problems for the equations of linear elasticity in the framework of meso-scale appr…
Green's kernels for transmission problems in bodies with small inclusions
Vladimir Maz'ya, Alexander Movchan, Michael Nieves
The uniform asymptotic approximation of Green's kernel for the transmission problem of antiplane shear is obtained for domains with small inclusions. The remainder estimates are pr…
Mesoscale asymptotic approximations to solutions of mixed boundary value problems in perforated domains
Vladimir Maz'ya, Alexander Movchan, Michael Nieves
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…