| Subject |
Inverse problems |
| Title |
Inverse Neumann problem for an equation of elliptic type |
| Author(s) |
Charyyar Ashyralyyev |
| Keywords |
difference scheme, overdetermination, well-posedness, stability, coercive stability |
| Abstract |
In this study, we consider inverse problem for an elliptic equation with Neumann conditions.
Stability and coercive stability estimates for the solution of inverse problem (1) are obtained. The first and second orders of accuracy difference schemes are presented. Stability and coercive stability inequalities for these difference schemes are given. In application, inverse problem for the multidimensional elliptic equation is studied. The first and second orders of accuracy difference schemes for the multidimensional inverse problem with overdetermination are presented. Well-posedness of both difference problems are established. The results are supported by numerical example for the two-dimensional elliptic equation.
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