| Title | 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 | 1 |
| SJR Quartile | 1 |
| JCR Impact | 1.91600 |
| SJR Impact | 1.07700 |
| 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 |
| Universidad Loyola members |
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