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http://bura.brunel.ac.uk/handle/2438/28525| Title: | Boundary-Domain Integral Equations for Variable-Coefficient Helmholtz BVPs in 2D |
| Authors: | Ayele, TG Demissie, BM Mikhailov, SE |
| Keywords: | Helmholtz equation;Dirichlet problem;mixed problem;parametrix;boundary-domain integral equations;equivalence;Fredholm properties. |
| Issue Date: | 30-May-2024 |
| Publisher: | Springer Nature |
| Citation: | Ayele, T.G., Demissie, B.M. and Mikhailov, S.E. (2024) 'Boundary-Domain Integral Equations for Variable-Coefficient Helmholtz BVPs in 2D', Journal of Mathematical Sciences, 280, pp. 300 - 335. doi: 10.1007/s10958-024-06993-6. |
| Abstract: | In this paper, we construct boundary-domain integral equations (BDIEs) of the Dirichlet and mixed boundary value problems for a two-dimensional variable-coefficient Helmholtz equation. Using an appropriate parametrix, these problems are reduced to several BDIE systems. It is shown that the BVPs and the formulated BDIE systems are equivalent. Fredholm properties and unique solvability and invertibility of BDIE systems are investigated in appropriate Sobolev spaces. |
| Description: | Data availability: There are no data associated with the manuscript to be made available. |
| URI: | https://bura.brunel.ac.uk/handle/2438/28525 |
| DOI: | https://doi.org/10.1007/s10958-024-06993-6 |
| ISSN: | 1072-3374 |
| Other Identifiers: | ORCiD: Sergey E. Mikhailov https://orcid.org/0000-0002-3268-9290 |
| Appears in Collections: | Dept of Mathematics Research Papers |
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