Under consideration is a nonlinear transport equation containing two nonlinearitiesand a coefficient $ q({\mathbf{x}}) $ of a lower-order nonlinear term depending on two or three space variables.We study the direct problem with the data on a part of the lateral surface of a cylindrical domain,explicitly construct a solution, and prove the uniqueness of the solution.Also, we state the problem of recoveringthe coefficient $ q({\mathbf{x}}) $ on some information about a solutionto the direct problem and demonstrate thatthe inverse problem reduces to an X-ray tomography problem.This opens a way to its efficient numerical solution.
