2 research outputs found
A new family of boundary‐domain integral equations for the Dirichlet problem of the diffusion equation in inhomogeneous media with H
Boundary-domain integral equations for variable coefficient Dirichlet BVP in 2D unbounded domain
In this paper, the Dirichlet boundary value problem for the second order
stationary diffusion elliptic partial differential equation with variable coefficient
is considered in unbounded (exterior) two dimensional domain. Using an appropriate
parametrix (Levi function), this problem is reduced to some direct segregated
Boundary-Domain Integral Equations (BDIEs).We investigate the properties of corresponding
parametrix-based integral volume and layer potentials in some weighted
Sobolev spaces, as well as the unique sovability of BDIEs and their equivalence to
the original BVP