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<p>In this paper, we investigate boundary-domain integral equations (BDIEs) for the Dirichlet boundary value problem (BVP) for Helmholtz equation with non-smooth coefficients on the Lipschitz domain. The equivalence of systems of BDIEs with the original problem, unique solvability of boundary-domain integral equations, and invertibility of boundary-domain integral operators are investigated in appropriate Sobolev spaces.</p>

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BOUNDARY-DOMAIN INTEGRAL EQUATIONS FOR NON-SMOOTH COEFFICIENT DIRICHLET PROBLEM FOR HELMHOLTZ EQUATION ON LIPSCHITZ DOMAIN

  • 期刊论文

  • 发表日期：

    2025年4月12日

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  • Shumatir Y. Monijore,
  • Mulugeta A. Dagnaw,
  • Tsegaye G. Ayele

摘要

In this paper, we investigate boundary-domain integral equations (BDIEs) for the Dirichlet boundary value problem (BVP) for Helmholtz equation with non-smooth coefficients on the Lipschitz domain. The equivalence of systems of BDIEs with the original problem, unique solvability of boundary-domain integral equations, and invertibility of boundary-domain integral operators are investigated in appropriate Sobolev spaces.