Determining of Coefficients and the Classical Solvability of a Nonlocal Boundary-Value Problem for the Benney–Luke Integro-Differential Equation with Degenerate Kernel.

Using the Fourier method of separation of variables, we examine the classical solvability and construct solutions of a nonlocal inverse boundary-value problem for the fourth-order Benney–Luke integro-differential equation with degenerate kernel. We prove the criterion of the unique solvability of the inverse boundary-value problem and examine the stability of solutions with respect to the recovery function. [ABSTRACT FROM AUTHOR]