Recovery of unknown coefficients in a two-dimensional hyperbolic
equation with additional conditions
In this paper, a nonlocal inverse boundary value problem for a
two-dimensional hyperbolic equation with overdetermination conditions is
studied. To investigate the solvability of the original problem, we
first consider an auxiliary inverse boundary value problem and prove its
equivalence (in a certain sense) to the original problem. Then using the
Fourier method, solving an equivalent problem is reduced to solving a
system of integral equations and by the contraction mappings principle
the existence and uniqueness theorem for auxiliary problem is proved.
Further, on the basis of the equivalency of these problems the uniquely
existence theorem for the classical solution of the considered inverse
problem is proved and some considerations on the numerical solution for
this inverse problem are presented with the examples.