FRESNEDA PORTILLO, CARLOS
No
Commun. Pure Appl. Anal
Article
Científica
1.916
1.077
01/07/2020
000565906000005
A system of Boundary-Domain Integral Equations is derived from the mixed (Dirichlet-Neumann) boundary value problem for the diffusion equation in inhomogeneous media defined on an unbounded domain. This paper extends the work introduced in [25] to unbounded domains. Mapping properties of parametrix-based potentials on weighted Sobolev spaces are analysed. Equivalence between the original boundary value problem and the system of BDIEs is shown. Uniqueness of solution of the BDIEs is proved using Fredholm Alternative and compactness arguments adapted to weigthed Sobolev spaces.
Variable coefficient; parametrix; unbounded domains; exterior problem; weighted Sobolev spaces; boundary-domain integral equations