BOUNDARY-DOMAIN INTEGRAL EQUATIONS FOR VARIABLE-COEFFICIENT HELMHOLTZ BVPs IN 2D
Tsegaye G. Ayele, Bizuneh M. Demissie, Sergey E. Mikhailov
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Source: Crossref
Published: Apr 1, 2024
DOI: 10.1007/s10958-024-06993-6
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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.
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