Analytic solutions for the Stephenʹʹs inverse problem with local boundary conditions including Elliptic and hyperbolic equations

In this paper, two inverse problems of Stephen kind with local (Dirichlet) boundary conditions are investigated. In the rst problem only a part of the boundary is unknown and in the second problem, the whole of the boundary is unknown. For both of the problems, rst, analytic expressions for unknown boundary are presented, then by using these analytic expressions for unknown boundaries and boundary conditions of the main problem, analytic solution of the main inverse problem is derived.