Measure solutions to the linear multi-dimensional transport equation with non-smooth coefficients

We are interested in the initial value problem This is the familiar (multi-dimensional) linear transport equation, in conservation form. We are going to assume a very weak regularity on the coefficients Obviously the characteristics X (t, x), given by have to be defined in a generalized sense. We choose the construction of Filippov, which is classically used in the context of conservation laws. Our definition requires the uniqueness of these generalized characteristics. To illustrate this point, two examples are considered. 19 refs.