2012/07/03 by A. G. Ramm, А. Г. Рамм, Ramm, A. G. · 1 citation
Computer Science · Engineering · Mathematics · Physics and Astronomy · #35J15 #35K20 #80A20 #80M40 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Composite Material Mechanics #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods in inverse problems #math-ph #math.AP #math.MP #msc:35J15 #msc:35K20 #msc:80A20 #msc:80M40
paper · pdf · doi:10.48550/arxiv.1207.0565
arxiv created 2012/07/03 · openalex publication_date 2012/07/03 · arxiv updated 2012/07/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The heat equation is considered in the complex system consisting of many small bodies (particles) embedded in a given material. On the surfaces of the small bodies a Newton-type boundary condition is imposed. An equation for the limiting field is derived when the characteristic size a of the small bodies tends to zero, their total number N(a) tends to infinity at a suitable rate, and the distance d = d(a) between neighboring small bodies tends to zero a << d. No periodicity is assumed about the distribution of the small bodies.