Analysis of Two-Operator Boundary-Domain Integral Equations for Variable-Coefficient Boundary Value Problems in 2D
| dc.contributor.advisor | Gedif, Tsegaye (PhD) | |
| dc.contributor.advisor | Mikhailov, Sergey E. (Professor) | |
| dc.contributor.author | Tesfaye, Solomon | |
| dc.date.accessioned | 2021-03-16T07:37:49Z | |
| dc.date.accessioned | 2023-11-04T12:31:12Z | |
| dc.date.available | 2021-03-16T07:37:49Z | |
| dc.date.available | 2023-11-04T12:31:12Z | |
| dc.date.issued | 2020-10-24 | |
| dc.description.abstract | In this dissertation, the boundary value problems (BVPs) for the second order elliptic partial differential equation with variable coefficient in two-dimensional bounded domain is considered. Using an appropriate parametrix (Levi function) and applying the two-operator approach (where the one operator approach fails ), the problems are reduced to some systems of boundary-domain integral equations (BDIEs). The two-operator BDIEs in 2D need a special consideration due to their different equivalence properties as compared to higher dimensional case due to the logarithmic term in the parametrix for the associated partial differential equation. Consequently, we need to set conditions on the domain or function spaces to insure the invertibility of the corresponding layer potentials, and hence the unique solvability of BDIEs. Equivalence of the two-operator BDIE systems to the original BVPs, BDIEs solvability, uniqueness/ non uniqueness of the solution, as well as Fredholm property and invertibility of the BDIEs are analysed. Moreover, the two-operator boundary domain integral operators for the Neumann BVP are not invertible, and appropriate finite-dimensional perturbations are constructed leading to invertibility of the perturbed operators. | en_US |
| dc.identifier.uri | http://etd.aau.edu.et/handle/123456789/25503 | |
| dc.language.iso | en | en_US |
| dc.publisher | Addis Ababa University | en_US |
| dc.subject | Analysis of Two-Operator | en_US |
| dc.subject | Boundary-Domain | en_US |
| dc.subject | Integral Equations | en_US |
| dc.subject | Variable-Coefficient | en_US |
| dc.subject | Boundary Value | en_US |
| dc.subject | Problems in 2D | en_US |
| dc.title | Analysis of Two-Operator Boundary-Domain Integral Equations for Variable-Coefficient Boundary Value Problems in 2D | en_US |
| dc.type | Thesis | en_US |