Problem of determining the source from a Hopf-type system

A one-dimensional inverse problem for a quasilinear hyperbolic system with an unknown excitation source is considered. The Cauchy problem for a nonlinear Hopf-type system is studied. The Fourier transform is used to reduce the inverse problem to a direct problem, and the existence and uniqueness theorem is proved. The approach used can become the basis for constructing an effective numerical algorithm for the inverse problem.