Well-posedness of Neumann type elliptic inverse problem with integral condition

In this thesis, the stability estimates for the solution of the Neumann type inverse problem with integral condition for elliptic differential equations in the an arbitrary Hilbert space have been investigated. Stability and coercive stability estimates will be obtained for solution of this problem. The first order of accuracy difference scheme for approximate solution of overdetermined elliptic problem will be constructed. Stability estimates for solution of difference scheme are obtained. Later, stability analysis for solution of Neumann type overdetermined problem with integral and Dirichlet conditions for multi-dimensional elliptic partial differential equation will be done. The first order of accuracy difference scheme for this problem will be constructed and stability analysis will be done. Algorithm for numerical solution of Neumann type overdetermined problem with integral for two-dimensional elliptic partial differential equation and MATLAB codes will be described. Key Words: Finite difference scheme, Well-posedness, Stability, Boundary Value Problem, Elliptic inverse problem, Overdetermination, Approximate solution, Integral condition