Mixed inverse problem for a Benney–Luke type integro-differential equation with two redefinition functions and parameters

Abstract

In this paper, we consider a linear Benney–Luke type partial integro-differential equation of higher order with degenerate kernel and two redefinition functions given at the endpoint of the segment and two parameters. To find these redefinition functions we use two intermediate data. Dirichlet boundary value conditions are used with respect to spatial variable. The Fourier series method of variables separation is applied. The countable system of functional-integral equations is obtained. Theorem on a unique solvability of countable system for functional-integral equations is proved. The method of successive approximations is used in combination with the method of contraction mapping. The triple of solutions of the inverse problem is obtained in the form of Fourier series. Absolutely and uniformly convergences of Fourier series are proved.

Keywords

• Inverse problem
• two redefinition functions
• final conditions
• intermediate functions
• Fourier method
• unique value solvability