DETERMINING OF COEFFICIENTS AND THE CLASSICAL SOLVABILITY OF A NONLOCAL BOUNDARY-VALUE PROBLEM FOR THE BENNEY-LUKE INTEGRO-DIFFERENTIAL EQUATION WITH DEGENERATE KERNEL

摘要

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.