An inverse problem for a nonlinear transport equation

Under consideration is a nonlinear transport equation containing two nonlinearities and 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 recovering the coefficient $q(\mathbf{x})$ on some information about a solution to the direct problem and demonstrate that the inverse problem reduces to an X-ray tomography problem. This opens a way to its efficient numerical solution.