Abstract
AbstractIn 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.
Publisher
Springer Science and Business Media LLC
Reference27 articles.
1. M.A. Al-Javary, L.C. Wrobel, Numerical solution of the two-dimensional Helmholtz equation with variable coefficients by the radial integration boundary integral and integro-differential equation methods. Internat. J. Computer Math., 89 (2012), 1463-1487.
2. T. G. Ayele, Analysis of two-operator boundary-domain integral equations for variable-coefficient mixed BVP in 2D with general right-hand side. J. Integral Equations Appl., 33 (2021), 403–426.
3. T. G. Ayele and S. T. Bekele, Two-operator boundary-domain integral equations for variable-coefficient mixed BVP in 2D. Math. Meth. Appl. Sci. 46 (2023) 12131–12154. https://doi.org/10.1002/mma.7971.
4. T. G. Ayele, T. T. Dufera and S. E. Mikhailov, Analysis of boundary-domain integral equations for variable-coefficient Neumann BVP in 2D. In: Integral Methods in Science and Engineering, Vol. 1, Constanda C. et al. (eds), Birkhäuser, Cham (2017), 21–32.
5. T. G. Ayele, T. T. Dufera and S. E. Mikhailov, Analysis of boundary-domain integral equations for variable-coefficient mixed BVP in 2D, In: Analysis, Probability, Applications, and Computation, K.-O. Lindahl et al. (eds.), (2019), 467–480.