Abstract:
An inverse problem for the elliptic equation of the second order with periodical boundary conditions is investigated. The definition
of a classical solution of the problem is introduced. The essence of the problem is that together with the solution it is
required to determine the unknown coefficient. The problem is considered in a rectangular domain. To investigate the solvability
of the inverse problem, the conversion from the original problem to the some direct auxiliary problem with trivial boundary
conditions is realized. Using the principle of condensed mappings, the existence and uniqueness of the solution of the auxiliary
problem are proved. The existence and uniqueness of the classical solution of the original problem are also proved.
Keywords:inverse boundary value problem, elliptic equation, Fourier method, classical solution.
Fulltext:
PDF file (351 kB)