2018/01/11 by Carlos Fresneda-Portillo, Carlos Fresneda‐Portillo, Sergey E. Mikhailov · 11 citations
Engineering · Mathematics · Physics and Astronomy · #Boundary value problem #Domain (mathematical analysis) #Electromagnetic Scattering and Analysis #Electromagnetic Simulation and Numerical Methods #Equivalence (formal languages) #Fourier integral operator #Integral equation #Mathematical analysis #Mathematics #Numerical methods in engineering #Parametrix #Partial differential equation #Pure mathematics #Sobolev space #math.AP #msc:31B10 #msc:35J25 #msc:45A05 #msc:45K05
paper · pdf · open access · doi:10.1080/17476933.2019.1591382
published in Complex Variables and Elliptic Equations 65(4), 558-572 (Taylor & Francis) · 15 pages
arxiv created 2018/01/11 · openalex publication_date 2019/04/08 · openalex created_date 2019/04/25 · arxiv updated 2020/11/23 · openalex updated_date 2026/07/02
A mixed boundary value problem (BVP) for the diffusion equation in non-homogeneous media partial differential equation is reduced to a system of direct segregated parametrix-based boundary-domain integral equations (BDIEs). We use a parametrix different from the one employed by Mikhailov [Localized boundary-domain integral formulations for problems with variable coefficients. Eng Anal Bound Elem. 2002;26:681–690], Mikhailov and Portillo [A new family of boundary-domain integral equations for a mixed elliptic BVP with variable coefficient. In: Paul Harris, editor. Proceedings of the 10th UK conference on boundary integral methods. Brighton: Brighton University Press; 2015. p. 76–84] and Chkadua, Mikhailov, Natroshvili [Analysis of direct boundary-domain integral equations for a mixed BVP with variable coefficient. I: equivalence and invertibility. J Integral Eqs Appl. 2009;21:499–543]. 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.