2020/03/30 by Carlos Fresneda-Portillo, Z. W. Woldemicheal, Zenebe W. Woldemicheal +1 · 2 citations
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Boundary value problem #Dirichlet integral #Dirichlet problem #Domain (mathematical analysis) #Heat equation #Integral equation #Numerical methods in engineering #Parametrix #Sobolev space #Thermoelastic and Magnetoelastic Phenomena #Uniqueness #math.AP #msc:31B10 #msc:35J25 #msc:45A05 #msc:45K05
paper · pdf · doi:10.1002/mma.6967
published in Mathematical Methods in the Applied Sciences 44(12), 9862-9875 (Wiley) · 17 pages
arxiv created 2020/03/30 · openalex created_date 2020/04/03 · openalex publication_date 2020/10/16 · arxiv updated 2020/11/23 · openalex updated_date 2026/08/05
A system of boundary‐domain integral equations (BDIEs) is obtained from the Dirichlet problem for the diffusion equation in nonhomogeneous media defined on an exterior two‐dimensional domain. We use a parametrix different from the one employed in Dufera and Mikhailov (2019). The system of BDIEs is formulated in terms of parametrix‐based surface and volume potentials whose mapping properties are analyzed in weighted Sobolev spaces. The system of BDIEs is shown to be equivalent to the original boundary value problem and uniquely solvable in appropriate weighted Sobolev spaces suitable for unbounded domains.