Siberian Federal University

The paper studies the two-dimensional problem of determining the kernel of the integral convolution operator that appears in the equation of acoustics with variable coefficients. The kernel function depends on the spatial and time variable. The direct problem is an initial-boundary problem for the acoustic pressure with zero initial data and a special Neumann boundary condition with a delta source of wave excitation. By linearization, applying the Fourier transform in the spatial variable, the inverse nonlinear problem is reduced to an equivalent system of linear Volterra integral equations of the second kind. In the space of continuous functions, the theorem of unique solvability is proved, and the stability estimate of the inverse problem solution is presented