Inverse Problem for a First-Order Hyperbolic System with Memory

For a first-order hyperbolic system of integro-differential equations with a convolution-type integral term, we study the inverse problem of determining the convolution kernel. The direct problem is an initial–boundary value problem for this system on a finite interval $$[0, H] $$ . Under some data consistency conditions, the inverse problem is reduced to a system of Volterra type integral equations. Further, the contraction mapping principle is applied to this system, and a theorem on the unique local solvability of the problem is proved for sufficiently small $$H$$ .