Inverse Boundary-Value Problem for an Integro-Differential Boussinesq-type Equation with Degenerate Kernel

We discuss questions on the unique solvability of inverse boundary-value source problems for a certain nonlinear integro-differential equation of Boussinesq type with degenerate kernel. We develop the method of degenerate kernels for the inverse boundary-value problem for a fourth-order integro-differential partial differential equation. Using the Banach fixed-point theorem, we prove the uniquely solvability of the problem and establish a criterion of stability of solutions with respect to recovery functions.