Green's Kernels and Meso-Scale Approximations in Perforated Domains

By Alexander Movchan, V.G. Maz'ya, Michael Nieves

Part I: Green's functions in singularly perturbed domains: Uniform asymptotic formulae for Green's functions for the Laplacian in domains with small perforations.- Mixed and Neumann boundary conditions for domains with small holes and inclusions. Uniform asymptotics of Green's kernels.- Green's function for the Dirichlet boundary value problem in a domain with several inclusions.- Numerical simulations based on the asymptotic approximations.- Other examples of asymptotic approximations of Green's functions in singularly perturbed domains.- Part II: Green's tensors for vector elasticity in bodies with small defects: Green's tensor for the Dirichlet boundary value problem in a domain with a single inclusion.- Green's tensor in bodies with multiple rigid inclusions.- Green's tensor for the mixed boundary value problem in a domain with a small hole.- Part III Meso-scale approximations. Asymptotic treatment of perforated domains without homogenization: Meso-scale approximations for solutions of Dirichlet problems.- Mixed boundary value problems in multiply-perforated domains.

• Format: Paperback
• Language: English
• ISBN: 3319003569
• ISBN13: 9783319003566
• Release Date: June 2013
• Publisher: Springer
• Length: 258 Pages
• Weight: 0.90 lbs.
• Dimensions: 0.7" x 6.0" x 9.0"