Analysis of Boundary-Domain Integral Equations to the mixed BVP for a compressible stokes system with variable viscosity

2018/05/01 by S. E. Mikhailov, Carlos Fresneda-Portillo, Sergey E. Mikhailov +1 · 17 citations
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Boundary value problem #Bounded function #Compressibility #Domain (mathematical analysis) #Equivalence (formal languages) #Integral equation #Numerical methods in engineering #Partial differential equation #Sobolev space #math.AP #msc:31B10 #msc:35J25 #msc:45A05 #msc:45K05 #msc:76N20

paper · pdf · open access · doi:10.3934/cpaa.2019137

published in Communications on Pure &amp Applied Analysis 18(6), 3059-3088 (American Institute of Mathematical Sciences)

arxiv created 2018/05/01 · openalex created_date 2018/05/07 · openalex publication_date 2019/01/01 · arxiv updated 2020/11/23 · openalex updated_date 2026/08/05

Abstract

The mixed boundary value problem for a compressible Stokes system of partial differential equations in a bounded domain is reduced to two different systems of segregated direct Boundary-Domain Integral Equations (BDIEs) expressed in terms of surface and volume parametrix-based potential type operators. Equivalence of the BDIE systems to the mixed BVP and invertibility of the matrix operators associated with the BDIE systems are proved in appropriate Sobolev spaces.

Cited by

• Analysis of boundary-domain integral equations based on a new parametrix for the mixed diffusion BVP with variable coefficient in an interior Lipschitz domain
• On the existence of solution of the boundary-domain integral equation system derived from the 2D Dirichlet problem for the diffusion equation with variable coefficient using a novel parametrix
• A new family of boundary‐domain integral equations for the Dirichlet problem of the diffusion equation in inhomogeneous media with H−1(Ω) source term on Lipschitz domains
• On the existence and uniqueness of solution of boundary‐domain integral equations for the Dirichlet problem for the nonhomogeneous heat transfer equation defined on a 2D unbounded domain