2018/09/09 by Sergey E. Mikhailov, S. E. Mikhailov, C. F. Portillo · 6 citations
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Boundary (topology) #Boundary value problem #Diffusion #Domain (mathematical analysis) #Equivalence (formal languages) #Lipschitz continuity #Lipschitz domain #Mathematical analysis #Mathematics #Numerical methods in engineering #Numerical methods in inverse problems #Parabolic partial differential equation #Parametrix #Partial differential equation #Physics #Pure mathematics #Variable (mathematics) #math.AP #msc:31B10 #msc:35J25 #msc:45A05 #msc:45K05
paper · pdf · doi:10.1216/jie.2020.32.59
published in Journal of Integral Equations and Applications 32(1) · arXiv admin note: text overlap with arXiv:1801.03854
arxiv created 2018/09/09 · openalex publication_date 2020/03/01 · arxiv updated 2020/11/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
A mixed boundary value problem for the partial differential equation of diffusion in an inhomogeneous medium in a Lipschitz domain is reduced to a system of direct segregated parametrix-based boundary-domain integral equations (BDIEs). We use a parametrix different from the one employed in previous papers by Mikhailov (2002, 2006) and Chkadua, Mikhailov and Natroshvili (2009). We prove the equivalence between the original BVP and the corresponding BDIE system. The invertibility and Fredholm properties of the boundary-domain integral operators are also analysed.