← Back
Publicaciones

A new family of boundary-domain integral equations for the diffusion equation with variable coefficient in unbounded domains

Authors

FRESNEDA PORTILLO, CARLOS

External publication

No

Means

Commun. Pure Appl. Anal

Scope

Article

Nature

Científica

JCR Quartile

✓

SJR Quartile

✓

JCR Impact

1.916

SJR Impact

1.077

Web

https://www.aimsciences.org/article/doi/10.3934/cpaa.2020228

Publication date

01/07/2020

ISI

000565906000005

DOI

10.3934/cpaa.2020228

Abstract

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.

Keywords

Variable coefficient; parametrix; unbounded domains; exterior problem; weighted Sobolev spaces; boundary-domain integral equations