Direct Boundary Integral Equation For Potential Equation With Dirichlet Boundary Conditions In 2d Piecewise Smooth Domain

Abstract

In this thesis, analysis of direct boundary integral equations(DBIEs) for potential equation subject to Dirichlet boundary condition in 2D were analyzed. Using fundamental solution in green’s identity, the considered Dirichlet boundary value problems is reduced to a system of boundary integral equations. Unique solvability of boundary integral equation system were proved. The equivalence of the obtained boundary integral equation systems to the original boundary value problems and invertiblity of the boundary integral equation operators were analyzed