Determination of a non-stationary adsorption coefficient analytical in part of spatial variables

The multidimensional adsorption coefficient inverse problem is considered for a second order hyperbolic equation. It is supposed that this coefficient is continuous with respect to the variables $t$, $x$ and analytic in the other spatial variables. For solving this equation, the scale method of Banach spaces of analytic functions is applied. The problem are reduced to a system of nonlinear Volterra integral equations and the local existence, global uniqueness, stability estimates are established.