A PROBLEM OF RECOVERING A SPECIAL TWO-DIMENSIONAL POTENTIAL IN A HYPERBOLIC EQUATION

We consider an inverse problem for partial differential equations of the second order related to recovering a coefficient (potential) in the lower term of this equations. It is supposed that the unknown potential is a trigonometric polynomial with respect to one of space variables with continuous coefficients of the other variable. The direct problem for the hyperbolic equation is the initial-boundary value problem for half-space x > 0 with zero initial Cauchy data and a special Neumann data at x = 0. We prove a local existence theorem for the inverse problem. The used method gives stability estimates for the solution to the direct and inverse problems and proposes a method of solving them.